We consider the dynamics of an isolated quantum many-body system after a sudden change of one control parameter, focusing on the statistics of the work done. We establish a connection between the generating function of the distribution of the work and the partition function of a classical system in a film geometry. Using this connection, we first show that the scaling of the fidelity susceptibilities close to a quantum phase transition can be understood in terms of the critical behavior of the excess entropy and specific heat in the classical model. Remarkably, we show that the statistics of the work close to the threshold and to criticality is connected to the so-called critical Casimir free energy which is responsible for the interaction between the boundaries of the classical system. On the basis of this relation, we highlight the emerging universal features of the statistics of the work. Our findings are exemplified for a global quench of the transverse Ising chain at zero temperature.
In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean fi…
We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force-free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing …
We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. We focus on the effect of corrections to scaling and probe numerically the universality of our results. In particular we check our hypothesis that corrections are well described by an effective thickness L_{0,eff}=L_0+c (L_0+L_s)^{1-ω} +L_s, where c and L_s are system specific parameters and ω\approx 0.8 is the exponent of the leading bulk correction. We simulate the improved Blume-Capel model and the Ising model on the simple cubic lattice. First we …
We show that work distributions and non-equilibrium work fluctuation theorems can be measured in optical spectra for a wide class of quantum systems. We consider systems where the absorption or emission of a photon corresponds to the sudden switch on or off of a local perturbation. For the particular case of a weak local perturbation, the Crooks relation establishes a universal relation in absorption as well as in emission spectra. Due to a direct relation between the spectra and work distribution functions this is equivalent to universal relations in work distributions for weak local quenches…
We study the crossover from the ordinary to the normal surface universality class in the three-dimensional Ising universality class. This crossover is relevant for the behavior of films of binary mixtures near the demixing point and a weak adsorption at one or both surfaces. We perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. We consider systems with film geometry, where various boundary conditions are applied. We discuss corrections to scaling that are caused by the surfaces and their relation with the so called extrapolation length. To this end w…
The finite-size renormalization-group approach for isotropic O$(n)$-symmetric systems introduced previously [V. Dohm, Phys. Rev. Lett. {\bf 110}, 107207 (2013)] is extended to weakly anisotropic O$(n)$-symmetric systems. Our theory is formulated within the $φ^4$ model with lattice anisotropy in a $d$-dimensional block geometry with periodic boundary conditions. It describes the crossover from low- to high-temperature fluctuations including Goldstone-dominated and critical fluctuations for $1\leq n \leq \infty$ in $2<d<4$ dimensions. An exact representation is derived for the large-distance beh…
Thermodynamic Casimir forces of film systems in the O$(n)$ universality classes with Dirichlet boundary conditions are studied below bulk criticality. Substantial progress is achieved in resolving the long-standing problem of describing analytically the pronounced minimum of the scaling function observed experimentally in $^4$He films $(n=2)$ by R. Garcia and M.H.W. Chan, Phys. Rev. Lett. ${\bf 83}, 1187 \;(1999)$ and in Monte Carlo simulations for the three-dimensional Ising model ($n=1$) by O. Vasilyev et al., EPL ${\bf 80}, 60009 \;(2007)$. Our finite-size renormalization-group approach yie…
We make an analytic investigation of rapid quenches of relevant operators in d-dimensional holographic CFT's, which admit a dual gravity description. We uncover a universal scaling behaviour in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory. Unless the amplitude of the quench is scaled appropriately, the work done on a system during the quench diverges in the limit of abrupt quenches for operators with dimension $\frac{d}{2} \leΔ< d$.
We study critical Casimir forces (CCF) $f_{\mathrm C}$ for films of thickness $L$ which in the three-dimensional bulk belong to the Ising universality class and which are exposed to random surface fields (RSF) on both surfaces. We consider the case that, in the absence of RSF, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We carry out a finite-size scaling analysis and show that for weak disorder CCF still exhibit scaling, acquiring a random field scaling variable $w$ which is zero for pure systems. We confirm these analytic predictions…
The confinement of long-ranged critical fluctuations in the vicinity of second-order phase transitions in fluids generates critical Casimir forces acting on confining surfaces or among particles immersed in a critical solvent. This is realized in binary liquid mixtures close to their consolute point $T_{c}$ which belong to the universality class of the Ising model. The deviation of the difference of the chemical potentials of the two species of the mixture from its value at criticality corresponds to the bulk magnetic filed of the Ising model. By using Monte Carlo simulations for this latter r…
The exact critical Casimir amplitude is derived for anisotropic systems within the $d=2$ Ising universality class by combining conformal field theory (CFT) with anisotropic $φ^4$ theory. Explicit results are presented for the general anisotropic scalar $φ^4$ model and for the fully anisotropic triangular-lattice Ising model in finite rectangular and infinite strip geometries with periodic boundary conditions (PBC). These results demonstrate the validity of multiparameter universality for confined anisotropic systems and the nonuniversality of the critical Casimir amplitude. We find an unexpect…
We numerically test an experimentally realizable method for the extraction of the critical Casimir force based on its thermodynamic definition as the derivative of the excess free energy with respect to system size. Free energy differences are estimated for different system sizes by integrating the order parameter along an isotherm. The method could be developed for experiments on magnetic systems and could give access to the critical Casimir force for any universality class. By choosing an applied field that opposes magnetic ordering at the boundaries, the Casimir force is found to increase b…
We study the thermodynamic Casimir force for films with various types of boundary conditions and the bulk universality class of the three-dimensional Ising model. To this end we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. In particular, we employ the exchange or geometric cluster cluster algorithm [J.R. Heringa and H. W. J. Blöte, Phys. Rev. E 57, 4976 (1998)]. In a previous work we demonstrated that this algorithm allows to compute the thermodynamic Casimir force for the plate-sphere geometry efficiently. It turns out that also for the film g…
We consider the decay of the thermodynamic Casimir force in phases with a finite correlation length. For the case of the strip, we use properties of low energy two-dimensional field theory to show that the decay depends on the symmetry properties of the boundary conditions, in distinctive ways that we determine exactly. Features characteristic of the bulk universality class may induce modifications that we also discuss. Symmetry breaking and symmetry preserving boundary conditions exchange their role with respect to the decay of the force when exchanging spontaneously broken with disordered ph…
We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++, where all spins at the boundary are fixed to +1 and +-, where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1. An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to …
We consider systems with slab geometry of finite thickness L that undergo second order phase transitions in the bulk limit and belong to the universality class of O(n)-symmetric systems with short-range interactions. In these systems the critical fluctuations at the bulk critical temperature T_c induce a long-range effective force called the "thermodynamic Casimir force". We describe the systems in the framework of the O(n)-symmetric phi^4-model, restricting us to the large-n limit n->infty. In this limit the physically relevant case of three space dimensions d=3 can be treated analytically in…
Using quasi-exact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h<>0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two discs. We find that varying the temperature along the iso-fields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a quali…
We study the large deviations statistics of the intensive work done by changing globally a control parameter in a thermally isolated quantum many-body system. We show that, upon approaching a critical point, large deviations well below the mean work display universal features related to the critical Casimir effect in the corresponding classical system. Large deviations well above the mean are, instead, of quantum nature and not captured by the quantum-to-classical correspondence. For a bosonic system we show that in this latter regime a transition from exponential to power-law statistics, anal…
We consider the effective pseudo-Casimir interaction forces mediated by a nematic liquid-crystalline film bounded by two planar surfaces, one of which imposes a random (disordered) distribution of the preferred anchoring axis in the so-called easy direction. We consider both the case of a quenched as well as an annealed disorder for the easy direction on the disordered surface and analyze the resultant fluctuation-induced interaction between the surfaces. In the case of quenched disorder, we show that the disorder effects appear additively in the total interaction and are dominant at intermedi…
Universality and weak-ergodicity breaking in quantum quenches
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institut für Theoretische Physik, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；CNR-INO（意大利国家研究委员会光电研究所）
An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. T…
We consider global quantum quenches, a protocol when a continuous field theoretic system in the ground state is driven by a homogeneous time-dependent external interaction. When the typical inverse time scale of the interaction is much larger than all relevant scales except for the UV-cutoff the system's response exhibits universal scaling behavior. We provide both qualitative and quantitative explanations of this universality and argue that physics of the response during and shortly after the quench is governed by the conformal perturbation theory around the UV fixed point. We proceed to calc…
We study the thermodynamic Casimir force between a spherical object and a plate. We consider the bulk universality class of the three-dimensional Ising model, which is relevant for experiments on binary mixtures. To this end, we simulate the improved Blume-Capel model. Following Hucht, we compute the force by integrating energy differences over the inverse temperature. We demonstrate that these energy differences can be computed efficiently by using a particular cluster algorithm. Our numerical results for strongly symmetry breaking boundary conditions are compared with the Derjaguin approxima…
We study the effects of scattering lengths on Lévy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact e…
We calculate the Casimir interaction between two parallel wires and between a wire and a metall plate. The dielectric properties of the objects are described by the plasma, Drude and perfect metal models. We find that at asymptotically large separation interactions involving plasma wires and/or plates are independent of the material properties, but depend on the dc conductivity $σ$ for Drude wires. Counterintuitively, at intermediate separations the interaction involving Drude wires can become independent of $σ$. At smaller separations, we compute the interaction numerically and observe an app…
We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T>T_c) the Casimir force decays exp…
The spatial suppression of order parameter fluctuations in a critical media produces Critical Casimir forces acting on confining surfaces. This scenario is realized in a critical binary mixture near the demixing transition point that corresponds to the second order phase transition of the Ising universality class. Due to these critical interactions similar colloids, immersed in a critical binary mixture near the consolute point, exhibit attraction. The numerical method for computation of the interaction potential between two spherical particles using Monte Carlo simulations for the Ising model…
We expand on the investigation of the universal scaling properties in the early time behaviour of fast but smooth quantum quenches in a general $d$-dimensional conformal field theory deformed by a relevant operator of dimension $Δ$ with a time-dependent coupling. The quench consists of changing the coupling from an initial constant value $λ_1$ by an amount of the order of $δλ$ to some other final value $λ_2$, over a time scale $δt$. In the fast quench limit where $δt$ is smaller than all other length scales in the problem, $ δt \ll λ_1^{1/(Δ-d)}, λ_2^{1/(Δ-d)}, δλ^{1/(Δ-d)}$, the energy (densi…
We study the crossover between thermodynamic Casimir forces arising from long-range fluctuations due to Goldstone modes and those arising from critical fluctuations. Both types of forces exist in the low-temperature phase of O$(n)$ symmetric systems for $n>1$ in a $d$-dimensional ${L_\parallel^{d-1} \times L}$ slab geometry with a finite aspect ratio $ρ= L/L_\parallel$. Our finite-size renormalization-group treatment for periodic boundary conditions describes the entire crossover from the Goldstone regime with a nonvanishing constant tail of the finite-size scaling function far below $T_c$ up …
We study the thermodynamic Casimir effect in thin films in the three dimensional XY universality class. To this end, we simulate the improved two component phi^4 model on the simple cubic lattice. We use lattices up to the thickness L_0=33. Based on the results of our Monte Carlo simulations we compute the universal finite size scaling function theta that characterizes the behaviour of the thermodynamic Casimir force in the neighbourhood of the critical point. We confirm that leading corrections to the universal finite size scaling behaviour due to free boundary conditions can be expressed by …
The three-dimensional quenched random bond diluted $(J_1-J_2)$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for $L \times L \times L$ lattice up to $L=48$. By employing standard finite-size scaling method, the numerical values of the Néel temperature are determined with high precision as a function of the coupling ratio $r=J_2/J_1$. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical $3…
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain $z=2.0245(15)$ for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our …
Motivated by recent experiments with confined binary liquid mixtures near their continous demixing phase transition we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically structured such that there is a laterally alternating adsorption preference for the species of the binary liquid mixture. By means of Monte Carlo simulations and finite-size scaling analysis we determine the critical Casimir force and the corresponding universal scaling function.
We investigate the effect of equilibrium topology on the statistics of non-equilibrium work performed during the subsequent unitary evolution, following a sudden quench of the Semenoff mass of the Haldane model. We show that the resulting work distribution function for quenches performed on the Haldane Hamiltonian with broken time reversal symmetry (TRS) exhibits richer universal characteristics as compared to those performed on the time-reversal symmetric massive graphene limit whose work distribution function we have also evaluated for comparison. Importantly, our results show that the work …
Analytic predictions have been derived recently by V. Dohm and S. Wessel, Phys. Rev. Lett. {\bf 126}, 060601 (2021) from anisotropic $φ^4$ theory and conformal field theory for the amplitude ${\cal F}_c$ of the critical free energy of finite anisotropic systems in the two-dimensional Ising universality class. These predictions employ the hypothesis of multiparameter universality. We test these predictions by means of high-precision Monte Carlo (MC) simulations for ${\cal F}_c$ of the Ising model on a square lattice with isotropic ferromagnetic couplings between nearest neighbors and with an an…
Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law sc…
Self-organized criticality in the Hwa-Kardar model of "running sandpile" [Phys. Rev. A 45, 7002 (1992)] with a turbulent motion of the environment taken into account is studied with the field theoretic renormalization group (RG). The turbulent flow is modelled by the synthetic $d$-dimensional anisotropic velocity ensemble introduced by Avellaneda and Majda [Commun. Math. Phys.131: 381 (1990)] with finite correlation time. The Hwa-Kardar model with time-independent (spatially quenched) random noise is considered alongside the original model with the white noise. The aim of the present paper is …
We discuss the relation of the specific heat, the energy density and the thermodynamic Casimir effect in the case of thin films in the three dimensional XY universality class. The finite size scaling function $θ(x)$ of the thermodynamic Casimir force can be expressed in terms of the scaling functions h'(x) and h(x) of the excess energy density and the excess free energy density. A priori these quantities depend on the reduced temperature t and the thickness L_0 of the film. However finite size scaling theory predicts that the scaling functions depend only on the combination x=t [L_0/ξ_0]^{1/ν}…
We consider the fluctuation-induced interaction of two thin, rod-like particles or "needles" immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length the mapping onto an annulus. For semi-infinite …
We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0, 1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimi…
We find a connection between logarithmic formation probabilities of two disjoint intervals of quantum critical spin chains and the Casimir energy of two aligned needles in two dimensional classical critical systems. Using this connection we provide a formula for the logarithmic formation probability of two disjoint intervals in generic $1+1$ dimensional critical systems. The quantity is depenedent on the full structure of the underlying conformal field theory and so useful to find the universality class of the critical system. The connection that we find also provides a very efficient numerica…
We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we demonstrate that in the case of a scalar field obeying Dirichlet or Neumann boundary conditions on the shell su…
