Experimentally there exist many materials with first-order phase transitions at finite temperature that display quantum criticality. Classically, a strain-energy density coupling is known to drive first-order transitions in compressible systems, and here we generalize this Larkin-Pikin mechanism to the quantum case. We show that if the T=0 system lies above its upper critical dimension, the line of first-order transitions ends in a "quantum annealed critical point" where zero-point fluctuations restore the underlying criticality of the order parameter. The generalized Larkin-Pikin phase diagram is presented and experimental consequences are discussed.
Experimentally there exist many materials with first-order phase transitions at finite temperature that display quantum criticality. Classically a strain-energy density coupling is known to drive first-order transitions in compressible systems, and here we generalize this Larkin-Pikin mechanism to the quantum case. We show that if the T=0 system lies above its upper critical dimension, the line of first-order transitions can end in a quantum annealed critical point where zero-point fluctuations restore the underlying criticality of the order parameter.
Motivated in part by quantum criticality in dissipative Kondo systems, we revisit the finite-size scaling of a classical Ising chain with 1/r^{2-epsilon} interactions. For 1/2<epsilon<1, the scaling of the dynamical spin susceptibility is sensitive to the degree of "winding" of the interaction under periodic boundary conditions. Infinite winding yields the expected mean-field behavior, whereas without any winding the scaling is of an interacting omega/T form. The contrast with the behavior of the Bose-Fermi Kondo model suggests a breakdown of a mapping from the quantum model to a classical one…
When a classical system is driven through a continuous phase transition, its nonequilibrium response is universal and exhibits Kibble-Zurek scaling. We explore this dynamical scaling in the novel context of a three-dimensional topological magnet with fractionalized excitations, namely the liquid-gas transition of the emergent mobile magnetic monopoles in dipolar spin ice. Using field-mixing and finite-size scaling techniques, we place the critical point of the liquid-gas line in the three-dimensional Ising universality class. We then demonstrate Kibble-Zurek scaling for sweeps of the magnetic …
The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires discontinuities. Numerous computer simulations have offered no proof of such transitions, however, instead finding deviations from expected scaling relations that were neither predicted by the DQC theory nor conform to standard scenarios. Here we show that this enigma can be resolved by introducing a critical scaling form with two divergent length scales. Simulatio…
We study the thermal and non-thermal steady state scaling functions and the steady-state dynamics of a model of local quantum criticality. The model we consider, i.e. the pseudogap Kondo model, allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points. In the vicinity of each fixed point we establish the existence of an effective temperature --different at each fixed point-- such that the equilibrium fluctuation-dissipation theorem is recovered. Most notably, steady-state scaling functions in terms of the effective temperatures coinci…
Numerical studies of the Néel to valence-bond solid phase transition in 2D quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realise the universal physics of the Neel-VBS transition in a 3D classical loop model (this includes the interference effect that suppresses Néel hedgehogs). We use this model to simulate unprecedentedly large systems (of size $L\leq 512$). Our results are compatible with a direct continuous transition at which both order par…
We derive exact expressions for the local entanglement entropy E in the ground state of the one-dimensional Hubbard model at a quantum phase transition driven by a change in magnetic field h or chemical potential u. The leading divergences of dE/dh and dE/du are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections to scaling signal a change in the number of local states accessible to the system as it undergoes the transition.
Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
Sun Yat-Sen University（中山大学）；Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所及凝聚态物理北京国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）；School of Physics and Materials Science, Guangzhou University（广州大学物理与材料科学学院）
Separation of the Kibble-Zurek Mechanism from Quantum Criticality
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究院）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学与应用研究所）；Max Planck Institute for the Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）
Different aspects of critical behaviour of magnetic materials are presented and discussed. The scaling ideas are shown to arise in the context of purely magnetic properties as well as in that of thermal properties as demonstrated by magnetocaloric effect or combined scaling of excess entropy and order parameter. Two non-standard approaches to scaling phenomena are described. The presented concepts are exemplified by experimental data gathered on four representatives of molecular magnets.
We report on ac magnetic susceptibility measurements under pressure of the Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that shows unconventional quantum criticality. In describing the susceptibility as $χ(T)^{-1} - χ(0)^{-1} \propto T^γ$, we find that $χ(0)^{-1}$ decreases with increasing pressure and vanishes to zero at the critical pressure $P_{\rm c} \simeq 2$ GPa, with $γ~ (\simeq 0.5)$ unchanged. We suggest that this quantum criticality emerges owing to critical valence fluctuations. Above $P_{\rm c}$, the approximant undergoes a magnetic transition at $T \si…
We analyze the quantum phase transition between a semimetal and a superfluid in a model of attractively interacting fermions with a linear dispersion. The quantum critical properties of this model cannot be treated by the Hertz-Millis approach since integrating out the fermions leads to a singular Landau-Ginzburg order parameter functional. We therefore derive and solve coupled renormalization group equations for the fermionic degrees of freedom and the bosonic order parameter fluctuations. In two spatial dimensions, fermions and bosons acquire anomalous scaling dimensions at the quantum criti…
The quantum criticality of the two-lead two-channel pseudogap Anderson model is studied. Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, $\propto |ω-μ_F|^r$ ($0<r<1$) near the Fermi energy. Equilibrium and non-equilibrium quantum critical properties at the two-channel Kondo (2CK) to local moment (LM) phase transition are addressed by extracting universal scaling functions in both linear and non-linear conductances, respectively…
Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige o…
Inspired by recent conflicting views on the order of the phase transition from an antiferromagnetic Neel state to a valence bond solid, we use the functional renormalization group to study the underlying quantum critical field theory which couples two complex matter fields to a non-compact gauge field. In our functional renormalization group approach we only expand in covariant derivatives of the fields and use a truncation in which the full field dependence of all wave-function renormalization functions is kept. While we do find critical exponents which agree well with some quantum Monte Carl…
Characterizing criticality in quantum many-body systems of dimension $\ge 2$ is one of the most important challenges of the contemporary physics. In principle, there is no generally valid theoretical method that could solve this problem. In this work, we propose an efficient approach to identify the criticality of quantum systems in higher dimensions. Departing from the analysis of the numerical renormalization group flows, we build a general equivalence between the higher-dimensional ground state and a one-dimensional (1D) quantum state defined in the imaginary time direction in terms of the …
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $π$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the cr…
We use the DBI action from string theory and holography to study the magneto-resistance at quantum criticality with hyperscaling violation. We find and analyze a rich class of scaling behaviors for the magneto-resistance. A special case describes the scaling results found in pnictides by Hayers et al. in~\cite{analytis}.
Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $μ$, effective magnetic field $H_1$, $H_2$ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent $z=2…
We compute the entanglement between separated blocks in certain spin models showing that at criticality this entanglement is a function of the ratio of the separation to the length of the blocks and can be written as a product of a power law and an exponential decay. It thereby interpolates between the entanglement of individual spins and blocks of spins. It captures features of correlation functions at criticality as well as the monogamous nature of entanglement. We exemplify invariant features of this entanglement to microscopic changes within the same universality class. We find this entang…
We study the finite temperature properties of quantum magnets close to a continuous quantum phase transition between two distinct valence bond solid phases in two spatial dimension. Previous work has shown that such a second order quantum `Lifshitz' transition is described by a free field theory and is hence tractable, but is nevertheless non-trivial. At $T>0$, we show that while correlation functions of certain operators exhibit $ω/T$ scaling, they do not show analogous scaling in space. In particular, in the scaling limit, all such correlators are purely {\em local} in space, although the sa…
The quantum phase transition to a $\mathbb{Z}_3$-ordered Kekulé valence bond solid in two-dimensional Dirac semimetals is governed by a fermion-induced quantum critical point, which renders the putatively discontinuous transition continuous. We study the resulting universal critical behavior in terms of a functional RG approach, which gives access to the scaling behavior on the symmetry-broken side of the phase transition, for general dimension and number of Dirac fermions. In particular, we investigate the emergence of the fermion-induced quantum critical point for space-time dimensions $2<d<…
A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, g_c < 1/2, and anomalous power laws for 1/2<g_c < 1, where g_c …
We demonstrate that the low-energy effective theory for a deconfined quantum critical point in $d=2+1$ dimensions contains a leading order contribution given by the Faddeev-Skyrme model. The Faddeev-Skyrme term is shown to give rise to the crucial Maxwell term in the CP$^1$ field theory governing the deconfined quantum critical point. We derive the leading contribution to the spin stiffness near the quantum critical point and show that it exhibits a logarithmic correction to scaling of the same type as recently observed numerically in low dimensional models of quantum spin systems featuring a …
We study a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of triangular and dual honeycomb lattice sites. In the classical ground state the spins on different sublattices are decoupled, but quantum and thermal fluctuations drive the system into a coplanar state via an "order from disorder" mechanism. We obtain the finite temperature phase diagram using renormalization group approaches. In the coplanar regime, the relative U$(1)$ phase between the spins on the two sublattices decouples from the remaining degrees of freedom, and is described by a six-sta…
We revisit an antiferromagnetic quantum phase transition with $\bm{Q} = 2 \bm{k}_{F}$, where $\bm{Q}$ is an ordering wave vector and $\bm{k}_{F}$ is a Fermi momentum. Reformulating the Hertz-Moriya-Millis theory within the strong coupling approach to diagonalize the spin-fermion coupling term and performing the scaling analysis for an effective field theory with quantum corrections in the Eliashberg approximation, we propose a novel interacting fixed point for this antiferromagnetic quantum phase transition, where antiferromagnetic spin fluctuations become locally critical to interact with ren…
We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point. We study both ground state and finite temperature properties. In two dimensions, the electrons and the order parameter fluctuations exhibit power-law scaling with anomalous scaling dimensions. The quasi-particle weight and the Fermi velocity vanish at the quantum critical point. The order parameter correlation length tur…
Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastab…
Quantum critical systems with multiple dynamics possess not only one but several time scales, tau_i ~ xi^(z_i), which diverge with the correlation length xi. We investigate how scaling predictions are modified for the simplest case of multiple dynamics characterized by two dynamical critical exponents, z_> and z_<. We argue that one should distinguish the case of coupled and decoupled multiple dynamic scaling depending on whether there exists a scaling exponent which depends on both z_i or not. As an example, we study generalized Phi^4-theories with multiple dynamics below their upper critical…
Unconventional quantum critical phenomena observed in Yb-based periodic crystals such as YbRh$_2$Si$_2$ and $β$-YbAlB$_4$ have been one of the central issues in strongly correlated electron systems. The common criticality has been discovered in quasicrystal Yb$_{15}$Au$_{51}$Al$_{34}$, which surprisingly persists under pressure at least up to $P=1.5$ GPa. The $T/H$ scaling where the magnetic susceptibility can be expressed as a single scaling function of the ratio of temperature $T$ and magnetic field $H$ has been discovered in the quasicrystal, which is essentially the same as that observed i…
We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction…
The magnetization, $M(H \leq 30$ T, 0.7 K $\leq T \leq 300$ K), from single crystals and powder samples of (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$ has been used to identify this system as an $S=1/2$ Heisenberg two-leg ladder in the strong coupling limit, $J_{\perp} = 13.3$ K and $J_{\parallel} = 3.8$ K, with $H_{c1} = 6.6$ T and $H_{c2} = 14.6$ T. An inflection point in $M(H, T = 0.7$ K) at half-saturation, $M_{s}/2$, is described by an effective \emph{XXZ} chain. The data exhibit universal scaling behavior in the vicinity of $H_{c1}$ and $H_{c2}$, indicating the system is near a quantum critical p…
The frequency dependence of the AC conductivity is studied in a holographic model of a non-fermi liquid that is amenable to both analytical and numerical computation. In the regime that dissipation dominates the DC conductivity, the AC conductivity is described well in the IR by a Drude peak despite the absence of quasiparticles. In the regime where pair-production-like processes dominate the conductivity there is no Drude peak. A scaling tail is found for the AC conductivity that is independent of the charge density and momentum dissipation. Evidence is given that this scaling tail $σ_{AC}\si…
We characterize quantum oscillations in the magnetic susceptibility of a quantum critical non-Fermi liquid. The computation is performed in a strongly interacting regime using the nonperturbative holographic correspondence. The temperature dependence of the amplitude of the oscillations is shown to depend on a critical exponent nu. For general nu the temperature scaling is distinct from the textbook Lifshitz-Kosevich formula. At the `marginal' value nu = 1/2, the Lifshitz-Kosevich formula is recovered despite strong interactions. As a by-product of our analysis we present a formalism for compu…
Quantum fluctuating loops in 2+1 dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins, or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is that the reconnection of a pair of strands is forbidden. This happens at previously-studied multi-critical points between topologically nontrivial phases. We show that this topologically constrained dynamics leads to universality classes with unusual scaling properties. For example, scaling operators…
Anomalous Quantum Criticality at a Continuous Metal-Insulator Transition
The Institute of Mathematical Sciences（马图拉科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Department of Physics, National Institute of Technology Agartala（阿格塔拉国立理工学院物理系）
We use the stochastic series expansion quantum Monte Carlo method to study the Heisenberg models on the square lattice with strong and weak couplings in the form of three different plaquette arrangements known as checkerboard models C$2\times2$, C$2\times4$ and C$4\times4$. The $a\times b$ here stands for the shape of plaquette consisting with spins connected by strong couplings. Through detailed analysis of finite-size scaling study, the critical point of C$2\times2$ model is improved as $g_{c}=0.548524(3)$ compared with previous studies with $g$ to be the ratio of weak and strong couplings i…
We develop a nonequilibrium increment method to compute the Rényi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that at an conformally-invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where although …
A holographic description on antiferromagnetic quantum phase transition (QPT) induced by magnetic field and the criticality in the vicinity of quantum critical point (QCP) have been investigated numerically recently. In this paper, we show that the properties of QPT in this holographic model are governed by a CFT dual to the emergent AdS$_2$ in the IR region, which confirms that the dual boundary theory is a strong coupling theory with dynamic exponent $z=2$ and logarithmic corrections appear. We also compare them with the results from Hertz model by solving RG equation at its upper critical d…
We study the optical conductivity sigma(Omega) of an electron system near a quantum-critical point with finite-wavelength ordering. sigma(Omega) vanishes in clean Galilean-invariant systems, unless electrons are coupled to dynamical collective modes, which dissipate the current. This coupling introduces a nonuniversal energy scale. Depending on the parameters of each specific system, a variety of responses arise near criticality: scaling peaks at a temperature- and doping-dependent frequency, peaks at a fixed frequency, or no peaks to be associated with criticality. Therefore the lack of scali…
The strange electronic state of a class of materials which violates the predictions of conventional Fermi-liquid theory of metals remains enigmatic. Proximity to a quantum critical point is a possible origin of this non-Fermi liquid (NFL) behavior, which is usually accomplished by tuning the ground state with non-thermal control parameters such as chemical composition, magnetic field or pressure. We present the spin dynamics study of a stoichiometric NFL system CeRhBi, using low-energy inelastic neutron scattering (INS) and muon spin relaxation (muSR) measurements. It shows evidence for an ene…
We study the out of equilibrium steady state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-$N$approach on the Keldysh contour, we study two different non-equilibrium setups: (a) a finite bias voltage and (b) a finite temperature gradient, imposed acro…
Quantum effects dominate the behaviour of many diverse materials. Of particular current interest are those systems in the vicinity of a quantum critical point (QCP). Their physical properties are predicted to reflect those of the nearby QCP with universal features independent of the microscopic details. The prototypical QCP is the Luttinger liquid (LL) which is of relevance to many quasi-one-dimensional materials. The magnetic material KCuF3 realizes an array of weakly-coupled spin chains (or LLs) and thus lies close to but not exactly at the Luttinger liquid quantum critical point. By using i…
We study a simple model of three-dimensional fermions close to a quadratic band touching point, built from the celebrated Luttinger single-particle Hamiltonian and an attractive contact interaction between the particles. Such a system displays a novel quantum critical point between the semimetallic and an s-wave superconducting phase at which the low-energy "Luttinger fermions" are inextricably coupled to the order parameter fluctuations. The quantum critical point is perturbatively accessible near four spatial dimensions, where it features nontrivial scaling with dynamical exponent 1<z<2 and …
We study the behavior of the entropy of the pseudogap Bose-Fermi Kondo model within a dynamical large-$N$ limit, where $N$ is related to the symmetry group of the model. This model is a general quantum impurity model that describes a localized level coupled to a fermionic bath having a density of states that vanishes in a powerlaw fashion near the Fermi energy and to a bosonic bath possessing a powerlaw spectral density below a cutoff energy. As a function of the couplings to the baths various quantum phase transitions can occur. We study how the impurity entropy changes across these zero-temp…
Metallic quantum criticality is a central theme in a variety of strongly correlated systems. Recent experiments have raised the fundamental question of how the charge response can be singular in cases where the Landau framework of quantum criticality allows singularity only in the spin channel. Motivated by this emerging issue, we study the particle-hole-asymmetric regime of a Bose-Fermi Anderson model with power-law forms for both the bosonic bath spectrum and the fermionic band density of states. We realize a particle-hole-asymmetric quantum-critical state where quasiparticles are lost due t…
The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents $β$ and $δ$ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states $N_{b}$. We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in $0<s<1/2$ and incurs the deviation of the exponents from the classi…
We report on susceptibility measurements in the strongly correlated layered cobalt oxide [BiBa0.66K0.36O2]CoO2, which demonstrate the existence of a magnetic quantum critical point (QCP) governing the electronic properties. The investigated low frequency susceptibility displays a scaling behavior with both the temperature T and the magnetic field B ranging from the high-T non-Fermi liquid down to the low-T Fermi liquid. Whereas the inferred scaling form can be discussed within the standard framework of the quantum critical phenomena, the determined critical exponents suggest an unconventional …
The scaling behavior over four decades of the ratio of temperature T to magnetic field B observed in the magnetization in beta-YbAlB4 is theoretically examined. By developing a theoretical framework that exhibits the quantum critical phenomena of Yb-valence fluctuations under a magnetic field, we show that the T/B-scaling behavior can appear near the quantum critical point of the valence transition. The emergence of the T/B scaling indicates the presence of the small characteristic energy scale of critical Yb-valence fluctuations. It is argued that the quantum valence criticality offers a unif…
We study disorder operator, defined as a symmetry transformation applied to a finite region, across a continuous quantum phase transition in $(2+1)d$. We show analytically that at a conformally-invariant critical point with U(1) symmetry, the disorder operator with a small U(1) rotation angle defined on a rectangle region exhibits power-law scaling with the perimeter of the rectangle. The exponent is proportional to the current central charge of the critical theory. Such a universal scaling behavior is due to the sharp corners of the region and we further obtain a general formula for the expon…
The long-thought charge Kondo effects have recently been experimentally realized in the quantum Hall regime. This experiment, supported by numerics, exemplifies the realization of two-channel Kondo state, a non-Fermi Liquid, and its crossover to the one-channel counterpart, a Fermi liquid. Scaling up such a platform, we find a hierarchy of non-Fermi Liquids and their tunable crossovers based on a renormalization group analysis. Utilizing results from a conformal field theory, we further examine the universal conductances of this strongly correlated system and their finite temperature scaling, …
