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arXiv:2407.05455 · Physical review. B./Physical review. B

Quantum supercritical crossover with dynamical singularity

Junsen Wang, Enze Lv, Xinyang Li, Yuliang Jin, Wei Li

Published Nov 17, 2025• 12 citations
arXivHTMLPDF

Abstract

Bounded by crossover lines exhibiting universal scaling, the supercritical regime above the critical end point is characterized by strong fluctuations and intriguing phenomena. In this study, we extend this notable concept of supercritical crossover to the quantum critical end point (QCEP), by studying the prototypical mixed-field quantum Ising and Potts models through tensor network calculations and scaling analyses. We reveal the existence of quantum supercritical (QSC) crossover lines, determined by not only response functions but also quantum information quantities, near the QCEP. A supercritical scaling law, $h\ensuremath{\sim}{(g\ensuremath{-}{g}_{c})}^{\mathrm{\ensuremath{\Delta}}}$, is found, where $g$ ($h$) is the transverse (longitudinal) field, ${g}_{c}$ is the critical field, and $\mathrm{\ensuremath{\Delta}}$ is the so-called gap exponent of the QCEP. Moreover, we demonstrate that the QSC crossover line acts as a boundary for the emergence of dynamical singularities in quench dynamics. This singularity manifests as a distinctive cusp with a critical exponent of 1/2, signaling a new dynamical universality class. We also propose utilizing Rydberg atom arrays as an experimental platform to observe these QSC crossovers and dynamical singularities. Our work establishes a theoretical framework for understanding the role of a QCEP and associated supercritical crossovers in both equilibrium and nonequilibrium quantum many-body systems.

DOI
10.1103/hgwk-pzw2

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Bounded by crossover lines exhibiting universal scaling, the supercritical regime above the critical end point is characterized by strong fluctuations and intriguing phenomena. In this study, we extend this notable concept of supercritical crossover to the quantum critical end point (QCEP), by studying the prototypical mixed-field quantum Ising and Potts models through tensor network calculations and scaling analyses. We reveal the existence of quantum supercritical (QSC) crossover lines, determined by not only response functions but also quantum information quantities, near the QCEP. A supercritical scaling law, h\ensuremath∼(g\ensuremath−gc)\ensuremathΔh\ensuremath{\sim}{(g\ensuremath{-}{g}_{c})}^{\mathrm{\ensuremath{\Delta}}}h\ensuremath∼(g\ensuremath−gc​)\ensuremathΔ, is found, where ggg (hhh) is the transverse (longitudinal) field, gc{g}_{c}gc​ is the critical field, and \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ is the so-called gap exponent of the QCEP. Moreover, we demonstrate that the QSC crossover line acts as a boundary for the emergence of dynamical singularities in quench dynamics. This singularity manifests as a distinctive cusp with a critical exponent of 1/2, signaling a new dynamical universality class. We also propose utilizing Rydberg atom arrays as an experimental platform to observe these QSC crossovers and dynamical singularities. Our work establishes a theoretical framework for understanding the role of a QCEP and associated supercritical crossovers in both equilibrium and nonequilibrium quantum many-body systems.
Abstract Quantum fluctuations can give rise to a singular quantum critical point (QCP) in the ground state, whose influence extends to finite temperatures, forming a quantum critical regime (QCR). Recently, it has been shown that in the quantum Ising model, the symmetry-breaking, longitudinal field can induce a quantum supercritical regime (QSR) emanating from the QCP, which hosts a universally enhanced quantum supercritical magnetocaloric effect (Lv et al 2025 Nat. Commun. 16 10646). In this paper, we show that the QSR also emerges in the spin-1/2 XXZ model, in both the forms of Ising and Berezinskii–Kosterlitz–Thouless (BKT) supercriticality. Using ground-state and finite-temperature tensor-network methods, we investigate quantum supercritical phenomena near a BKT QCP. We reveal a quantum supercritical crossover scaling T ∝ h 2 / 3 and a Grüneisen ratio scaling Γ h ∝ T − 3 / 2 for the BKT QCP, which differ from the corresponding Ising supercritical scalings. Nevertheless, we find that the scaling function ϕ Γ ( x ) of the singular Grüneisen ratio for both BKT and Ising cases can be approximately described by the same expression ϕ Γ ( x ) ≈ x / ( 1 + x 2 ) . Our work extends the study of quantum supercritical phenomena from the Ising to the XXZ Heisenberg model, thereby revealing the presence of BKT quantum supercriticality and broadening the scope of quantum supercritical physics.
Abstract Quantum critical points (QCPs) ubiquitously emerge in strongly correlated systems, with their influence extending beyond zero temperature. There exist extended quantum critical regimes (QCRs) at finite temperatures and external fields. A paradigmatic example exhibiting QCP is quantum Ising magnets like CoNb 2 O 6 , where critical quantum fluctuations and robust universal scaling behavior provide crucial insights into the quantum material. In this work, we discover a fundamentally distinct quantum supercritical regime (QSR) emerging also from the QCP but controlled by symmetry-breaking fields (h) coupled to the order parameter. The QSR is enclosed by the crossover boundaries T~h zν/Δ , where z, ν and Δ≡β+γ are critical exponents. Amongst other intriguing phenomena, there exists an enhanced magnetocaloric effect (MCE) in QSR, characterized by a universally diverging magnetic Gr\"uneisen ratio Γ h ≡1/T(∂T/∂h) S ~T -Δ/zν . Even small symmetry-breaking fields generate dramatic temperature variations. The supercritical scaling can be comprehended via thermal data collapse based on the derived scaling form. We propose to observe the QSR and related supercritical MCE in CoNb 2 O 6 and other quantum Ising magnets, which may enable cryogenic technologies capable of reaching the millikelvin regime without relying on helium-3.
Quantum fluctuations can give rise to a singular quantum critical point (QCP) in the ground state, whose influence extends to finite temperatures, forming a quantum critical regime (QCR). Recently, it has been shown that in the quantum Ising model, the symmetry-breaking, longitudinal field can induce a quantum supercritical regime (QSR) emanating from the QCP, which hosts a universally enhanced quantum supercritical magnetocaloric effect (MCE). In this paper, we show that the QSR also emerges in the spin-1/2 XXZ model, in both the form of Ising and Berezinskii-Kosterlitz-Thouless (BKT) supercriticality. Using ground-state and finite-temperature tensor-network methods, we investigate quantum supercritical phenomena near a BKT QCP. We reveal a quantum supercritical crossover scaling T∝h2/3T \propto h^{2/3}T∝h2/3 and a Grüneisen ratio scaling Γh∝T−3/2Γ_h \propto T^{-3/2}Γh​∝T−3/2 for the BKT QCP, which differ from the corresponding Ising supercritical scalings. Nevertheless, we find that the scaling function ϕΓ(x)ϕ_Γ(x)ϕΓ​(x) of the singular Grüneisen ratio for both BKT and Ising cases can be approximately described by the same expression ϕΓ(x)≈x/(1+x2)ϕ_Γ(x) \approx x/(1+x^2)ϕΓ​(x)≈x/(1+x2). Our work extends the study of quantum supercritical phenomena from the Ising to the XXZ Heisenberg model, thereby revealing the presence of BKT quantum supercriticality and broadening the scope of quantum supercritical physics.
Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.
Extracting critical behavior in the wake of quantum quenches has recently been at the forefront of theoretical and experimental investigations in condensed matter physics and quantum synthetic matter, with particular emphasis on experimental feasibility. Here, we investigate the potential of single-site observables in probing equilibrium phase transitions and dynamical criticality in short-range transverse-field Ising chains. For integrable and near-integrable models, our exact and mean-field-theory analyses reveal a truly out-of-equilibrium universal scaling exponent in the vicinity of the transition that is independent of the initial state and the location of the probe site so long as the latter is sufficiently close to the edge of the chain. Signature of a dynamical crossover survives when integrability is strongly broken. Our work provides a robust scheme for the experimental detection of quantum critical points and dynamical scaling laws in short-range interacting models using modern ultracold-atom setups.
Dynamical detection of quantum phases and phase transitions (QPTs) in quenched systems with experimentally convenient initial states is a topic of interest from both theoretical and experimental perspectives. Quenched from polarized states, longitudinal magnetization decays exponentially to zero in time for the short-range transverse-field Ising model and hence has a featureless steady state regime, which prevents it from exhibiting dynamical phase transitions of type I. In this paper, we ask whether the transient regimes of such nonequilibrium processes probed by single-site observables, that is magnetization per site, could encode information about the underlying QPT. The decay rates of time-dependent and single-site observables exhibit a dynamical crossover that separates two dynamical regions, ordered and disordered, both of which have distinct nonequilibrium responses. We construct a dynamical order parameterlike quantity that exhibits a scaling law in the vicinity of the crossover. Our results reveal that scaling law exponent in short times in the close vicinity of the dynamical crossover is significantly different than the one predicted by analytical theory for long times. When integrability is strongly broken, the crossover boundary turns into a region that separates two other dynamical regions that act like dynamically ordered and disordered regimes.