Nonmonotonic response and light-cone freezing in fermionic systems under quantum quenches from gapless to gapped or partially gapped states

Abstract

The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a Generalized Gibbs Ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, non-monotonic response of steady state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the non-monotonous behaviour of observables. In continuum non-interacting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favour of the robustness of the phenomenon in the cases of non-sudden quenches and higher dimensionality.PACS numbers: 67.85. Lm, 05.70.Ln, 71.70.Ej, 05.30.Fk Non-equilibrium quantum physics is at the heart of most relevant applications of solid state physics, such as transistors and lasers [1][2][3] . More fundamentally, one of the main difficulties in studying many-body non-equilibrium quantum physics is represented by the unavoidable interactions that any quantum system has with its surroundings. This coupling is difficult to control and causes an effectively non-unitary evolution even on short time scales 4 . The recent advent of cold atom physics 5 allowed not only to access quantum systems characterized by weak coupling to the environment, but also to engineer Hamiltonians which show non-ergodic behavior 6,7 : the so called integrable systems 8 . Moreover, in the context of cold atom physics, it is possible to manipulate the parameters of the Hamiltonian in a time dependent and controllable fashion 7,9-12 . The combination of these three ingredients gave rise to a renewed interest in the physics of quantum quenches [13][14][15][16][17] , which led to the birth of a new thermodynamic ensemble, the Generalized Gibbs Ensemble (GGE) 1,[18][19][20][21]23 . Quantum quenches have been studied in a wide range of systems with the property that a change in a parameter of the Hamiltonian deeply affects the physical properties of the system itself. Interaction quenches in Luttinger liquids [24][25][26][27][28][29][30][31][32][33][34][35][36] and magnetic field quenches in the one-dimensional (1D) Ising model [37][38][39][40][41][42][43][44][45][46][47] are prominent examples in this direction. Furthermore, at the level of free fermions, quantum quenches between gapped phases characterized by different Chern numbers have also been studied [48][49][50][51] . However, not much attention has been devoted to the study of quantum quenches between gapless and gapped states. A notable exception is represented by quantum quenches from a Luttinger liquid to a sine-Gordon model [52][53][54][55][56][57][58][59][60][61] and quantum time mirrors 62 . However...

Topological classification of dynamical quantum phase transitions in the xy chain

“…Aside from issues related to thermalization, that are mostly inspected by means of the long time behaviour of the systems, quantum quenches are also interesting at finite times. In translational invariant systems, two point correlators are characterized by a light-cone structure 37 – 41 . This intriguing phenomenon is related to the fact that information can only propagate at finite velocity.…”

A Short Review of One-Dimensional Wigner Crystallization

“…The experimental consequences of the Luttinger liquid behavior of fermionic systems can be found in very different contexts, ranging from Bechgaard salts [24,25], to quantum wires [26][27][28][29], quantum Hall edges [30][31][32], quantum spin Hall edges [33,34], and carbon nanotubes [35], even in the presence of mechanical vibrations [36,37]. Interestingly, strongly out of equilibrium scenarios can also be inspected within this framework [38][39][40][41][42][43][44][45][46][47][48][49]. While genuine long range order cannot be established at non-zero temperature, typical correlation lengths exceeding the size of the sample have been conjectured in very diverse contexts [50][51][52][53][54] and are responsible for the so called one-dimensional Wigner molecule.…”

A Short Review on One Dimensional Wigner Crystallization

“…The experimental consequences of the Luttinger liquid behavior of fermionic systems can be found in very different contexts, ranging from Bechgaard salts [24,25], to quantum wires [26][27][28][29], quantum Hall edges [30][31][32], quantum spin Hall edges [33,34], and carbon nanotubes [35], even in the presence of mechanical vibrations [36,37]. Interestingly, strongly out of equilibrium scenarios can also be inspected within this framework [38][39][40][41][42][43][44][45][46][47][48][49]. Although genuine long range order cannot be established at non-zero temperature, typical correlation lengths exceeding the size of the sample have been conjectured in very diverse contexts [50][51][52][53][54] and are responsible for the so called one-dimensional Wigner molecule.…”