Quantum Criticality: When Matter Becomes Infinitely Sensitive

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1. Introduction: The Thermodynamics of Absolute Zero

The study of phases of matter has historically been the study of thermal competition. In the classical paradigm of condensed matter physics, the state of a system is determined by the minimization of free energy, $F = U – TS$, where the internal energy $U$ favors order and the entropy $S$, driven by temperature $T$, favors disorder. Phase transitions, such as the melting of ice or the demagnetization of iron, occur when the entropic contribution overwhelms the energetic benefits of order. However, a profound shift in our understanding of matter occurs when we consider the limit of absolute zero. At $T=0$, entropy vanishes for a perfectly ordered system, and thermal fluctuations cease. Yet, Heisenberg’s uncertainty principle dictates that a quantum system can never be truly at rest. Zero-point motion—quantum fluctuations—persists. When these quantum fluctuations are tuned by a non-thermal control parameter, such as pressure, magnetic field, or chemical doping, they can drive the system between distinct ground states. The singularity separating these ground states is the Quantum Critical Point (QCP).1

Quantum criticality is not merely a zero-temperature curiosity; it is a regime of “infinite sensitivity.” As a system approaches a QCP, the energy difference between the ground state and the lowest excited states vanishes, leading to a divergence in the susceptibility to external perturbations.1 The correlation length $\xi$, representing the spatial distance over which degrees of freedom are entangled, diverges. Unlike classical transitions, where statics and dynamics can often be decoupled, quantum phase transitions (QPTs) are inherently dynamic. The temporal correlation length $\xi_\tau$ also diverges, linked to the spatial correlation length by a dynamic critical exponent $z$, such that $\xi_\tau \sim \xi^z$.3 This entwining of space and time creates a “quantum critical fan” that extends upward from the QCP into the finite temperature phase diagram, governing the physical properties of materials up to surprisingly high temperatures and giving rise to exotic states of matter, including non-Fermi liquid “strange metals” and high-temperature superconductors.5

This report provides an exhaustive analysis of the physics of quantum criticality. We will explore the breakdown of the conventional Landau-Ginzburg-Wilson paradigm, the emergence of fractionalized excitations in Deconfined Quantum Critical Points (DQCP), and the microscopic mechanisms driving “strange metal” behavior near the Planckian dissipation limit. Through detailed case studies of heavy fermion compounds like YbRh$_2$Si$_2$ and CeCoIn$_5$, as well as high-$T_c$ cuprates and pnictides, we elucidate how the infinite sensitivity of the quantum critical state serves as the crucible for the most enigmatic phenomena in modern condensed matter physics.

2. The Standard Model and Its Discontents: From Landau to Hertz-Millis

2.1 The Landau-Ginzburg-Wilson (LGW) Paradigm

For much of the 20th century, the understanding of phase transitions was codified by the Landau-Ginzburg-Wilson (LGW) theory. This framework rests on the concept of spontaneous symmetry breaking. A phase transition is defined by the onset of a local order parameter $\phi(\mathbf{r})$—a quantity that is zero in the disordered phase but acquires a finite vacuum expectation value in the ordered phase.7 For a ferromagnet, this is the magnetization vector; for a superconductor, it is the complex gap function.

The LGW functional expands the free energy density in powers of the order parameter and its gradients, assuming that the transition is driven by long-wavelength thermal fluctuations. The critical behavior—the universality class—is determined solely by the dimensionality of the system ($d$) and the symmetry of the order parameter ($N$).7 Renormalization group (RG) analysis shows that as the critical point is approached, irrelevant microscopic details flow to zero, leaving a scale-invariant fixed point characterized by universal critical exponents.9

However, the LGW framework faces a fundamental challenge when applied to quantum phase transitions: the statics and dynamics can no longer be separated. In classical statistical mechanics, the partition function is a sum over static configurations weighted by the Boltzmann factor. In quantum mechanics, the non-commutativity of the Hamiltonian operators necessitates a path integral formulation in imaginary time $\tau$. The system effectively acquires an extra dimension, behaving like a classical system in $d+z$ dimensions.11

2.2 The Hertz-Millis-Moriya Framework

The extension of LGW theory to metallic quantum critical points was pioneered by Hertz (1976) and refined by Millis (1993) and Moriya. The Hertz-Millis-Moriya (HMM) theory integrates out the fermionic degrees of freedom (the conduction electrons) to derive an effective action for the bosonic order parameter $\phi$.12

The resulting effective action takes the form:

 

$$S_{eff}[\phi] \propto \sum_{\mathbf{q}, \omega_n} \chi^{-1}(\mathbf{q}, \omega_n) |\phi(\mathbf{q}, \omega_n)|^2 + u \int d\mathbf{r} d\tau \phi^4$$

 

where the inverse susceptibility $\chi^{-1}$ contains a dynamical term proportional to $|\omega_n| / q^{z-2}$ (for antiferromagnets) or $|\omega_n|/q$ (for ferromagnets), reflecting the Landau damping of spin fluctuations by the conduction electrons.12

A crucial prediction of HMM theory concerns the “effective dimension” of the transition, $d_{eff} = d + z$.

  • For a clean itinerant ferromagnet, the dynamical exponent is $z=3$ (due to Landau damping). In three spatial dimensions ($d=3$), the effective dimension is $d+z=6$.
  • For an itinerant antiferromagnet, $z=2$, yielding $d_{eff} = 5$ in 3D.

Standard RG arguments state that if $d_{eff}$ is greater than the upper critical dimension (typically $d_c^+ = 4$ for $\phi^4$ theory), the nonlinear interactions between fluctuations (the $u\phi^4$ term) become irrelevant. The fixed point is Gaussian (mean-field). Therefore, HMM theory predicts that most metallic QPTs should exhibit mean-field critical exponents, modified only by logarithmic corrections.12

2.3 The Breakdown of Hertz-Millis

While HMM theory successfully describes transitions in some itinerant magnets like spin-density-wave transitions in chromium, it fails spectacularly in strongly correlated Heavy Fermion systems and high-$T_c$ superconductors. The failure arises from the assumption that the fermions can be safely integrated out.

In reality, the coupling between the critical bosonic mode and the gapless excitations on the Fermi surface is singular. At an antiferromagnetic QCP, “hot spots”—points on the Fermi surface connected by the ordering wavevector $\mathbf{Q}$—experience intense scattering. This can destroy the coherence of the quasiparticles, leading to a breakdown of the Fermi liquid description itself.12 The feedback of the critical bosons onto the fermions, and vice versa, leads to a “non-Fermi liquid” state where the effective mass diverges and the quasiparticle weight $Z$ vanishes. This necessitates a theory that treats the fermionic and bosonic degrees of freedom on equal footing, rather than integrating one out. The experimental signatures of this breakdown—such as the fractional power-law divergence of the Grüneisen ratio in YbRh$_2$Si$_2$—point to a new class of universality beyond the Landau-Ginzburg-Wilson-Hertz-Millis paradigm.16

3. Deconfined Quantum Criticality: Fractionaling the Order

One of the most radical departures from standard critical theory is the concept of Deconfined Quantum Critical Points (DQCP), proposed by Senthil et al. This framework addresses transitions between two ordered phases that break distinct, unrelated symmetries—a scenario where LGW theory strictly predicts a first-order transition (or an intermediate phase).7

3.1 The Forbidden Transition

Consider a two-dimensional square lattice quantum magnet. It can order as a Néel Antiferromagnet (AFM), where spins align in a checkerboard pattern (breaking spin rotation symmetry $SU(2)$ but preserving lattice symmetries). Alternatively, it can form a Valence Bond Solid (VBS), where spins pair into singlets on bonds (preserving spin rotation but breaking lattice translation symmetry).

According to Landau theory, to transition continuously from AFM to VBS, one would effectively need to tune two independent parameters to simultaneously vanish both order parameters at the same point—a “multicritical” coincidence that is generic impossible.

However, computational and theoretical evidence suggests such continuous transitions do exist. The resolution lies in deconfinement. At the critical point, the order parameters of both phases are revealed to be composite objects formed from more fundamental, fractionalized particles called spinons.17

3.2 Mechanism of Deconfinement

In the DQCP framework, the fundamental degrees of freedom at the transition are spin-$1/2$ bosons (spinons) $z_\alpha$ coupled to an emergent $U(1)$ gauge field $A_\mu$.

  • The Néel Order: The magnetic order parameter $\vec{N}$ is a bilinear of spinons: $\vec{N} = z^\dagger \vec{\sigma} z$.
  • The VBS Order: The VBS order parameter $\psi_{VBS}$ corresponds to the creation operator for a purely magnetic flux (monopole) of the emergent gauge field.

In the AFM phase, the spinons are “confined” (bound into magnons) because the gauge field implies a potential that grows linearly with separation. In the VBS phase, spinons are also confined into valence bonds. However, exactly at the critical point, the confinement length diverges. The spinons become free (“deconfined”) interacting via the gauge field. The transition is not between two orders, but a phase transition of the spinons themselves.

3.3 Experimental and Numerical Evidence

Recent numerical simulations on the “J-Q model” (Heisenberg exchange $J$ plus multi-spin interaction $Q$) strongly support the existence of DQCP. They observe:

  • Emergent Symmetry: The system exhibits an emergent $SO(5)$ symmetry at the critical point, which rotates the 3-component Néel vector and the 2-component VBS vector into each other, unifying the two disparate broken symmetries.7
  • Anomalous Exponents: The critical exponents found (e.g., $\eta$) are large and distinct from any classical universality class (like Heisenberg or Ising).

Experimentally, the Shastry-Sutherland compound SrCu$_2$(BO$_3$)$_2$ is a primary candidate. Under high pressure, it transitions from a dimer singlet phase (VBS-like) to an AFM phase. Recent specific heat and neutron scattering experiments suggest a proximate DQCP, evidenced by scaling behaviors consistent with fractionalized excitations rather than conventional magnons.19 Similarly, recent studies on Quantum Hall Bilayers have identified a continuous transition between an exciton superfluid and a stripe phase that fits the DQCP phenomenology, identifying a critical dynamical exponent $z \approx 1$.20

4. Local Quantum Criticality and the Kondo Breakdown

While DQCP modifies the bosonic sector, another route to non-LGW criticality involves the direct breakdown of the electronic fluid itself. This is the Local Quantum Critical Point (or Kondo Breakdown) scenario, primarily observed in Heavy Fermion materials.

4.1 The Heavy Fermion Dilemma

Heavy fermion systems contain a lattice of localized $f$-electrons (from Rare Earths like Ce, Yb) embedded in a sea of conduction electrons ($c$-electrons). The physics is dictated by the competition between two interactions:

  1. Kondo Effect ($T_K$): The $c$-electrons screen the $f$-moments, forming heavy, neutral quasiparticles. The $f$-electrons become part of the Fermi surface (Large Fermi Surface).
  2. RKKY Interaction ($T_{RKKY}$): An indirect magnetic exchange that aligns the $f$-moments into magnetic order (usually AFM), keeping them localized (Small Fermi Surface).

In the standard Hertz-Millis picture (Itinerant SDW type), the Kondo effect remains intact across the QCP. The $f$-electrons remain part of the Fermi surface, and only the magnetic ordering wavevector becomes critical (“hot spots”).

In the Local QCP picture, the Kondo effect itself collapses exactly at the magnetic QCP. The $f$-electrons suddenly localize, removing themselves from the Fermi volume.22

4.2 Hall Effect Anomalies

The most direct evidence for Local Criticality comes from Hall effect measurements in YbRh$_2$Si$_2$.

  • Observation: Upon tuning the magnetic field through the critical value $B_c$, the Hall coefficient $R_H$ exhibits a sharp, discontinuous jump (in the $T \to 0$ limit).
  • Interpretation: $R_H$ is inversely proportional to the carrier density $n$. A jump implies a sudden change in $n$, consistent with the “Large” to “Small” Fermi surface reconstruction. This jump scales with the width of the quantum critical region, providing evidence that the critical fluctuations are not just long-wavelength spin waves (as in HMM) but involve the breakup of the heavy quasiparticles themselves.22

This “Kondo breakdown” implies that the critical fluctuations are local in real space (involving the screening cloud of each $f$-atom), leading to a form of “local quantum criticality” where the anomalous dimension $\eta$ in space is small, but the correlations in time are highly singular.16

5. The Phenomenology of Strange Metals

Perhaps the most ubiquitous and perplexing signature of quantum criticality is the “strange metal” phase. Observed in cuprates, pnictides, and heavy fermions, this state is defined by transport properties that violate the fundamental tenets of Fermi Liquid theory.

5.1 The Linear-in-$T$ Resistivity

In a normal metal, electrical resistivity $\rho(T)$ at low temperatures is dominated by electron-electron scattering ($\propto T^2$) or electron-phonon scattering ($\propto T^5$). In strange metals, $\rho(T)$ scales linearly with temperature:

 

$$\rho(T) = \rho_0 + A T$$

 

This linearity persists over vast temperature ranges—in some cuprates like Bi2212, from the superconducting $T_c$ (~90 K) up to 1000 K.24

This behavior is problematic for the quasiparticle concept. As the temperature increases, the scattering rate $\Gamma$ increases. At high enough temperatures, the mean free path $l$ of the electrons (distance traveled between collisions) becomes shorter than the interatomic spacing $a$ (or the de Broglie wavelength). In a Boltzmann transport picture, a particle cannot scatter before it has even propagated a single lattice site. This condition is known as the Mott-Ioffe-Regel (MIR) limit. Strange metals routinely violate the MIR limit, with resistivities continuing to rise linearly well beyond the point where $l < a$. This proves that the charge carriers are not coherent quasiparticles but an incoherent, collective quantum fluid.25

5.2 The Planckian Dissipation Limit

The universality of the $T$-linear resistivity has led to the hypothesis of a fundamental quantum bound on dissipation. The scattering rate $1/\tau$ in these systems appears to be determined solely by temperature and fundamental constants:

 

$$\frac{1}{\tau} \approx \alpha \frac{k_B T}{\hbar}$$

 

where $\alpha$ is a constant of order unity ($0.7 \lesssim \alpha \lesssim 1.2$) across a wide variety of materials. This timescale, $\tau_{\hbar} = \hbar / k_B T$, is the Planckian time. It represents the fastest possible rate at which a quantum system can thermalize or “scramble” information.26

Table 1: Planckian Dissipation Parameters in Strange Metals

(Derived from experimental data in 24)

Material Tc​ (K) Effective Mass m∗/me​ Scattering Rate Coefficient α Resistivity Exponent n (ρ∝Tn)
YbRh$_2$Si$_2$ 0.002 $\sim 1000$ (diverges) $\approx 1.0$ 1.0 (near QCP)
CeCoIn$_5$ 2.3 $\sim 300$ $\approx 0.8 – 1.2$ 1.0 (at $H_{c2}$)
Bi-2212 (Cuprate) 90 8.4 $1.1 \pm 0.3$ 1.0
LSCO (Cuprate) 40 9.8 $1.2 \pm 0.4$ 1.0
BaFe$_2$(As,P)$_2$ 30 ~5-10 $\approx 1.0$ 1.0 (at optimal doping)

The fact that $\alpha \approx 1$ across materials with effective masses differing by factors of 100 (from cuprates to heavy fermions) suggests that the mechanism is independent of the specific microscopic details (band structure, lattice parameters) and is a generic property of the quantum critical state.25

5.3 Holographic Connections (AdS/CFT)

The Planckian time $\hbar/k_B T$ also appears in black hole physics. A black hole’s event horizon scrambles quantum information at exactly this rate. This coincidence has fueled the application of the AdS/CFT correspondence (holographic duality) to condensed matter. In this view, the strange metal in $d$ spatial dimensions is dual to a black hole in $d+1$ dimensions. The infinite sensitivity of the critical point corresponds to the geometry near the black hole horizon. While controversial, this approach provides one of the few analytical tools capable of deriving the linear-in-$T$ resistivity and MIR violation from first principles.25

6. Case Studies in Material Realization

To ground these theories, we examine the materials that host these phenomena. The physical realization of quantum criticality requires extreme purity and precise tuning.

6.1 YbRh$_2$Si$_2$: The Prototypical Local QCP

Ytterbium Rhodium Silicide (YbRh$_2$Si$_2$) is the most studied heavy fermion quantum critical metal. It orders antiferromagnetically at a very low temperature ($T_N = 0.07$ K). A small magnetic field of $B_c = 0.06$ T (applied in the basal plane) suppresses this order to zero, creating a QCP.23

  • Divergent Grüneisen Ratio: The Grüneisen ratio $\Gamma = \alpha_{vol} / C_p$ (ratio of thermal expansion to specific heat) is a sensitive probe of pressure dependence. At a QCP, $\Gamma$ is predicted to diverge as $T^{-1/\nu z}$. In YbRh$_2$Si$_2$, $\Gamma$ diverges as $T^{-0.7}$ to $T^{-1.0}$, indicating a singular accumulation of entropy that persists down to the lowest measurable temperatures ($< 20$ mK).16
  • Multiple Energy Scales: The system exhibits distinct crossover lines in the $T-B$ phase diagram. The $T^*$ line, where the Hall coefficient jumps, merges with the $T_N$ line exactly at the QCP, supporting the scenario that the breakup of heavy fermions (Kondo destruction) drives the magnetic transition.22

6.2 CeCoIn$_5$: Criticality Inside the Dome

Cerium Cobalt Indium-5 (CeCoIn$_5$) is a $d$-wave superconductor with $T_c = 2.3$ K. It is unique because the QCP appears to be “hidden” by the superconducting phase.

  • Field-Tuned Criticality: When a magnetic field $H \approx 5$ T suppresses superconductivity, the normal state reveals non-Fermi liquid behavior ($\rho \sim T$, $C/T \sim -\ln T$). This suggests a field-induced QCP exactly at $H_{c2}$.30
  • Zn-Doping Revelation: Substituting minute amounts of Zinc (Zn) for Indium suppresses superconductivity and reveals the underlying magnetic ground state. These experiments show that the projected AFM QCP is located inside the superconducting dome. This implies that the superconducting state is not just a dome “masking” the QCP, but that the quantum critical fluctuations are integral to the formation of the condensate itself.32
  • Dimensional Crossover: Thermal transport measurements suggest a crossover from 2D fluctuations (at higher $T$) to 3D fluctuations (at low $T$) near the QCP, highlighting the role of anisotropic coupling in layered heavy fermions.16

6.3 Iron-Based Superconductors (Pnictides)

In the pnictides, such as BaFe$2$(As${1-x}$P$_x$)$_2$, the QCP separates an orthorhombic antiferromagnetic phase from a tetragonal paramagnetic phase.

  • Strange Metal Hall Effect: Unlike simple metals where the Hall coefficient $R_H$ is constant, in critical pnictides, $R_H$ becomes strongly temperature dependent. Specifically, the cotangent of the Hall angle follows $\cot \theta_H \propto T^2$, while resistivity $\rho \propto T$. This “two-lifetime” phenomenology suggests that charge current and Hall current decay via different mechanisms, a signature of the anisotropic scattering expected from critical spin fluctuations (“hot spots” vs “cold spots” on the Fermi surface).33
  • Nematic Criticality: The phase transition involves both spin (magnetic) and orbital (nematic) degrees of freedom. The critical fluctuations are “nematic”—fluctuations of the lattice symmetry breaking—which may enhance pairing in the $s_\pm$ channel.35

7. Universality Classes: A Comprehensive Catalog

The classification of quantum phase transitions relies on identifying the universality class, defined by the critical exponents ($\nu, z, \alpha, \beta, \gamma, \eta$).

Table 2: Universality Classes of Quantum Phase Transitions

(Synthesized from 8)

Universality Class Symmetry Dyn. Exp. z ν (Correlation) β (Order) Physical Examples
Transverse Field Ising $Z_2$ 1.0 1.0 (1D), 0.63 (3D) 0.32 (3D) LiHoF$_4$, CoNb$_2$O$_6$
Quantum XY $U(1)$ 1.0 (Insulator) 0.67 (3D) 0.35 (3D) Superfluid-Insulator Trans.
Quantum Heisenberg $O(3)$ 1.0 (Insulator) 0.71 (3D) 0.36 (3D) TlCuCl$_3$ (Pressure tuned)
Itinerant AFM (Hertz) $O(3)$ 2.0 0.5 (Mean Field) 0.5 Clean AFM Metals (Theory)
Itinerant FM (Hertz) $O(3)$ 3.0 0.5 (Mean Field) 0.5 Clean FM Metals (Theory)
Local Criticality $SU(2) \times U(1)$ $\approx 0.7-1$ Fractional Varies YbRh$_2$Si$_2$ (Kondo breakdown)
Deconfined (DQCP) $SO(5)$ (emergent) $\approx 1.0$ Varies (Large $\eta$) Varies SrCu$_2$(BO$_3$)$_2$
Quantum Hall Topological $\approx 1.0$ $\approx 2.4$ N/A Integer/Fractional QH Transition

Key Insight on Exponents:

The dynamical exponent $z$ is the discriminator between classes.

  • $z=1$: Space and time scale equally. This is typical for insulators or transitions where the order parameter does not decay into particle-hole pairs (Lorentz invariant effective action).
  • $z=2$: Dynamics are diffusive. Typical for antiferromagnets in metals where spin waves decay into electron-hole pairs (Landau damping).
  • $z=3$: Dynamics are extremely slow/overdamped. Typical for ferromagnets in metals ($q=0$ conservation laws limit decay).
  • Fractional/Effective $z$: In strange metals, experimental fits often yield fractional exponents (e.g., $z \approx 4/3$ or dynamic scaling $E/T$), indicating a departure from the simple Gaussian fixed points of Hertz-Millis theory.4

8. Superconductivity: The Child of Criticality

The most practical consequence of quantum criticality is the generation of unconventional superconductivity. In almost all strange metals, the QCP is shrouded by a superconducting dome.

8.1 The “Glue” Mechanism

In BCS theory, phonons provide the attractive potential $V$. In quantum critical systems, the divergent magnetic susceptibility $\chi(\mathbf{q}, \omega)$ implies giant spin fluctuations. The effective interaction between electrons becomes:

 

$$V_{eff}(\mathbf{q}, \omega) \sim – g^2 \chi(\mathbf{q}, \omega)$$

 

Since $\chi$ diverges at the QCP, the pairing interaction strength $\lambda$ is massively enhanced.

  • Symmetry Matching: The interaction is repulsive in the $s$-wave channel (electrons repel) but can be attractive in anisotropic channels ($d$-wave or $s_{\pm}$) where the gap function changes sign on the Fermi surface to avoid the Coulomb penalty.39

8.2 Why a Dome?

If the interaction diverges at the QCP, why doesn’t $T_c$ go to infinity? Why does it form a dome that peaks near but often not at the QCP?

  1. Coherence vs. Interaction: While the pairing glue (interaction strength) increases towards the QCP, the scattering rate (pair breaking) also increases. The quasiparticles become short-lived (incoherent). Superconductivity requires well-defined quasiparticles to form coherent pairs. The dome peak represents the “sweet spot” where the interaction is strong but the quasiparticles are still sufficiently coherent.41
  2. Competing Orders: Near the QCP, other phases (CDW, stripes, nematicity) also compete for the same Fermi surface density of states, suppressing $T_c$ right at the critical point.42

8.3 The Pseudogap Precursor

In cuprates, the region above the superconducting dome (the underdoped side) exhibits a “pseudogap”—a partial suppression of the density of states without long-range order.

  • Quantum Fluctuation Origin: Numerical studies (Quantum Monte Carlo on FM rotor models) suggest the pseudogap can arise from pre-formed pairs or strong pairing fluctuations in the quantum critical regime. The system tries to superconductor, opening a gap, but phase coherence is destroyed by the intense quantum fluctuations.41
  • Symmetry Breaking: Alternative theories propose the pseudogap is a distinct phase (e.g., loop currents, nematicity) that ends at a QCP inside the dome, distinct from the magnetic QCP.36

9. Conclusion

Quantum criticality represents the regime where matter is pushed to its absolute limits of sensitivity. By tuning a zero-temperature control parameter, we access a singularity where the collective behavior of billions of electrons is dictated not by the details of the crystal lattice, but by the universal laws of quantum entanglement and information scrambling.

The journey from the standard Hertz-Millis theory to the modern landscapes of Deconfined Quantum Criticality and Planckian Dissipation reflects a maturing understanding of many-body physics. We have learned that:

  1. Local vs. Itinerant: The fate of the electron itself—whether it remains itinerant or localizes—is a key variable in the critical theory (Kondo breakdown).
  2. Strange Metals are Universal: The Planckian bound $\tau \sim \hbar/k_B T$ suggests a deep link between condensed matter criticality and the fundamental limits of quantum dynamics, potentially bridging the gap to quantum gravity.
  3. Criticality Breeds Superconductivity: The quantum critical fan is not just a region of disorder; it is the breeding ground for the strongest electron pairing known to science.

As experimental techniques improve—allowing us to probe noise, thermal transport, and spectral functions with ever-higher resolution at ever-lower temperatures—the “infinite sensitivity” of the quantum critical point will continue to reveal the deepest secrets of quantum matter. The ultimate goal remains: to harness this sensitivity to design materials where these critical correlations survive to room temperature, ushering in a new era of quantum technologies.