Quantum Phase Transitions Go Dynamical

Abstract

The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production. DOI: 10.1103/PhysRevLett.119.080501 Today, the equilibrium properties of quantum matter are theoretically described with great success. Yet, in recent years pioneering experiments have created quantum states beyond this equilibrium paradigm [1,2]. Thanks to this progress, it is now possible to experimentally study exotic phenomena such as many-body localization [3,4], prethermalization [5,6], particle-antiparticle production in the lattice Schwinger model [7], and light-induced superconductivity [8]. Understanding general properties of such nonequilibrium quantum states provides a significant challenge, calling for concepts that extend important principles such as universality to the nonequilibrium realm. A general approach towards this major goal is the theory of dynamical quantum phase transitions (DQPTs) [9], which extends the concept of phase transitions and thus universality to the nonequilibrium regime. In this Letter, we directly observe the defining real-time nonanalyticities at DQPTs in a trapped-ion quantum simulator for interacting transverse-field Ising models. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.Statistical mechanics and thermodynamics provide us with an excellent understanding of equilibrium quantum many-body systems. A key concept in this framework is the canonical partition function ZðTÞ ¼ Trðe −H=k B T Þ, with T being the temperature, k B the Boltzmann constant, and H the system Hamiltonian. The partition function encodes thermodynamics via the free-energy density f ¼ −ðk B T=NÞ log ½ZðTÞ , where N denotes the number of degrees of freedom.A phase transition, i.e., a sudden change of macroscopic behavior, is associated with a nonanalytical behavior of f as a function of temperature or another control parameter g such as an external magnetic field. QPTs [10] occur when T is kept at absolute 0, where the system's ground-state properties undergo a nonanalytic change as a function of g [see Fig. 1(a)]. Scenarios where boundary conditions are essential, such as for the Casimir effect, can be studied by boundary partition functions Z B ¼ hψ 0 je −RH jψ 0 i, where jψ 0 i encodes the spatial boundary conditions on two ends of the system at dis...

Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals

“…In contrast to conventional Anderson transitions [36,37], the disorder-averaged nodal density of states (NDOS) in disordered WSMs is deemed an appropriate order parameter by field-theoretical calculations [30,[38][39][40], as well as the numerical observation of its sharp power-law growth above some critical disorder strength [24,25,41]. However, recent studies of nonperturbative instantonic effects have revealed that rare disorder configurations lift the NDOS and round out its critical behavior [28,42,43], thus challenging the conventional scenario. A physical picture was then put forward by Nandkishore et al [42], who associated the NDOS lift to smooth rare regions of a random potential landscape that can sporadically bound eigenstates at the nodal energy, giving way to an exponentially small but nonzero NDOS.…”

Dynamical quantum phase transitions in extended transverse Ising models

“…Following the initial proposal, there have been an upsurge of studies probing the possibility of DQPTs in different integrable and non-integrable models [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. (For review see [55][56][57]). It has also been shown that the occurrence of DQPTs is not necessarily entangled with the equilibrium quantum critical point (QCP) for both integrable [58] and non-integrable models [59].…”

Dynamical quantum phase transitions in extended toric-code models

“…One of the exciting consequences of such quantum quenches is the dynamical quantum phase transitions (DQPTs) [35]. This concept has been well studied for various systems [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] (for review see [51][52][53][54]), notably for instance, in the context of one-dimensional transverse field Ising-model (TFIM) [63][64][65]. In the one-dimensional Ising model, the dynamical counterpart of free energy density was observed to exhibit non-analyticities (cusp singularities) at critical times, during the consequent real-time unitary evolution (dictated by the final Hamiltonian following the quench) of the ground state of the pre-quenched Hamiltonian.…”