Search

We examine the behavior of the entanglement asymmetry in the ground state of a (1+1)-dimensional conformal field theory with a boundary condition that explicitly breaks a bulk symmetry. Our focus is on the asymmetry of a subsystem $A$ originating from the symmetry-breaking boundary and extending into a semi-infinite bulk. By employing the twist field formalism, we derive a universal expression for the asymmetry, showing that the asymptotic behavior for large subsystems is approached algebraically, with an exponent which is twice the conformal dimension of a boundary condition-changing operator. As a secondary result, we also establish a similar asymptotic behavior for the string order parameter. Our exact analytical findings are validated through numerical simulations in the critical Ising and 3-state Potts models., Comment: 20 pages, 5 figures. v2: fixed typos and added references

Bipartite entanglement entropy is one of the most useful characterizations of universal properties in a many-body quantum system. Far from equilibrium, there exist two highly effective theories describing its dynamics -- the quasiparticle and membrane pictures. In this work we investigate entanglement dynamics, and these two complementary approaches, in a quantum circuit model perturbed by an impurity. In particular, we consider a dual unitary quantum circuit containing a spatially fixed, non-dual-unitary impurity gate, allowing for differing local Hilbert space dimensions to either side. We compute the entanglement entropy for both a semi-infinite and a finite subsystem within a finite distance of the impurity, comparing exact results to predictions of the effective theories. We find that for a semi-infinite subsystem, both theories agree with each other and the exact calculation. For a finite subsystem, however, both theories qualitatively differ, with the quasiparticle picture predicting a non-monotonic growth in contrast to the membrane picture. We show that such non-monotonic behavior can arise even in random chaotic circuits, pointing to a hitherto unknown shortcoming of the membrane picture in describing such systems., Comment: 5+7 pages, 2+1 figures. v2: Added a section to the Supplemental Material, updated acknowledgments; 5+9 pages, 2+3 figures

The entanglement asymmetry is an observable independent tool to investigate the relaxation of quantum many body systems through the restoration of an initially broken symmetry of the dynamics. In this paper we use this to investigate the effects of interactions on quantum relaxation in a paradigmatic integrable model. Specifically, we study the dynamical restoration of the $U(1)$ symmetry corresponding to rotations about the $z$-axis in the XXZ model quenched from a tilted ferromagnetic state. We find two distinct patterns of behaviour depending upon the interaction regime of the model. In the gapless regime, at roots of unity, we find that the symmetry restoration is predominantly carried out by bound states of spinons of maximal length. The velocity of these bound states is suppressed as the anisotropy is decreased towards the isotropic point leading to slower symmetry restoration. By varying the initial tilt angle, one sees that symmetry restoration is slower for an initally smaller tilt angle, signifying the presence of the quantum Mpemba effect. In the gapped regime however, spin transport for non maximally tilted states, is dominated by smaller bound states with longer bound states becoming frozen. This leads to a much longer time scales for restoration compared to the gapless regime. In addition, the quantum Mpemba effect is absent in the gapped regime., Comment: 19+5 pages, 5 figures

The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by local, few-body terms. Unfortunately, in non-equilibrium situations, analytic results are rare and largely confined to continuous field theories, which fail to accurately describe microscopic models. To address this gap, we present an exact analytic result for the EH following a generic quantum quench in non-interacting fermionic models. This derivation adapts the celebrated quasiparticle picture to the EH, providing detailed insights into its physical properties. The resulting analytic formula serves as a foundation for engineering EHs in quantum optics experiments., Comment: 7 pages, 2 figures

The finite parts of a large, locally interacting many-body system prepared out-of-equilibrium eventually equilibrate. Characterising the underlying mechanisms of this process and its timescales, however, is particularly hard as it requires to decouple universal features from observable-specific ones. Recently, new insight came by studying how certain symmetries of the dynamics that are broken by the initial state are restored at the level of the reduced state of a given subsystem. This provides a high level, observable-independent probe. Until now this idea has been applied to the restoration of internal symmetries, e.g. U(1) symmetries related to charge conservation. Here we show that that the same logic can be applied to the restoration of space-time symmetries, and hence can be used to characterise the relaxation of fully generic systems. We illustrate this idea by considering the paradigmatic example of "generic" many-body dynamics, i.e. a local random unitary circuit. We show that, surprisingly, the restoration of translation symmetry in these systems only happens on time-scales proportional to the subsystem's volume. In fact, for large enough subsystems the time of symmetry restoration becomes initial-state independent (as long as the latter breaks the symmetry at time zero) and coincides with the thermalisation time. For intermediate subsystems, however, one can observe the so-called "quantum Mpemba effect", where the state of the system restores a symmetry faster if it is initially more asymmetric., Comment: 6+4 pages, 3 figures

Local relaxation after a quench in 1-D quantum many-body systems is a well known and very active problem with rich phenomenology. Except for pathological cases, the local relaxation is accompanied by the local restoration of the symmetries broken by the initial state that are preserved by the unitary evolution. Recently, the entanglement asymmetry has been introduced as a probe to study the interplay between symmetry breaking and relaxation in an extended quantum system. In particular, using the asymmetry, it has been shown that the more a symmetry is initially broken, the faster it may be restored. This surprising effect, which has been also observed in trapped-ion experiments, can be seen as a quantum version of the Mpemba effect and is manifested by the crossing at a finite time of the entanglement asymmetry curves of two different initial symmetry breaking configurations. In this paper we show, how, by tuning the initial state, the symmetry dynamics in free fermionic systems can display much richer behaviour than seen previously. In particular, for certain classes of initial states, including ground states of free fermionic models with long-range couplings, the entanglement asymmetry can exhibit multiple crossings. This illustrates that the existence of the quantum Mpemba effect can only be inferred by examining the late time behaviour of the entanglement asymmetry., Comment: 25 pages, 5 figures

Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and in particular the latter are independent of the model parameters. Using the quasi-particle picture we obtain the full time evolution of the cumulants and find that although their endpoints are fixed, the finite time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct non-trivial and non-Gaussian fluctuations and large deviations., Comment: 19 pages, 8 figures, 1 appendix

The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that non-equilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here we study a quantum version of the Mpemba effect that takes place in closed many body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model., Comment: 6+8 pages, 2+2 figures; v2 as appears in Phys. Rev. Lett

Topological excitations or defects such as solitons are ubiquitous throughout physics, supporting numerous interesting phenomena like zero energy modes with exotic statistics and fractionalized charges. In this paper, we study such objects through the lens of symmetry-resolved entanglement entropy. Specifically, we compute the charge-resolved entanglement entropy for a single interval in the low-lying states of the Su-Schrieffer-Heeger model in the presence of topological defects. Using a combination of exact and asymptotic analytical techniques, backed up by numerical analysis, we find that, compared to the unresolved counterpart and to the pure system, a richer structure of entanglement emerges. This includes a redistribution between its configurational and fluctuational parts due to the presence of the defect and an interesting interplay with entanglement equipartition. In particular, in a subsystem that excludes the defect, equipartition is restricted to charge sectors of the same parity, while full equipartition is restored if the subsystem includes the defect, as long as the associated zero mode remains unoccupied. Additionally, by exciting zero modes in the presence of multiple defects, we observe a significant enhancement of entanglement in certain charge sectors, due to charge splitting on the defects. The two different scenarios featuring the breakdown of entanglement equipartition are underlied by a joint mechanism, which we unveil by relating them to degeneracies in the spectrum of the entanglement Hamiltonian. In addition, equipartition is shown to stem from an equidistant entanglement spectrum., Comment: 17 pages, 7 figures and 4 appendices

Conserved-charge densities are very special observables in quantum many-body systems as, by construction, they encode information about the dynamics. Therefore, their evolution is expected to be of much simpler interpretation than that of generic observables and to return universal information on the state of the system at any given time. Here we study the dynamics of the fluctuations of conserved U(1) charges in systems that are prepared in charge-asymmetric initial states. We characterise the charge fluctuations in a given subsystem using the full-counting statistics of the truncated charge and the quantum entanglement between the subsystem and the rest resolved to the symmetry sectors of the charge. We show that, even though the initial states considered are homogeneous in space, the charge fluctuations generate an effective inhomogeneity due to the charge-asymmetric nature of the initial states. We use this observation to map the problem into that of charge fluctuations on inhomogeneous, charge-symmetric states and treat it using a recently developed space-time duality approach. Specialising the treatment to interacting integrable systems we combine the space-time duality approach with generalised hydrodynamics to find explicit predictions., Comment: 30 pages, 8 figures; v2 presentation significantly improved; v3 as appears in Phys. Rev. B

Quantum impurity models (QIMs) are ubiquitous throughout physics. As simplified toy models they provide crucial insights for understanding more complicated strongly correlated systems, while in their own right are accurate descriptions of many experimental platforms. In equilibrium, their physics is well understood and have proven a testing ground for many powerful theoretical tools, both numerical and analytical, in use today. Their non-equilibrium physics is much less studied and understood. However, the recent advancements in non equilibrium integrable quantum systems through the development of generalized hydrodynamics (GHD) coupled with the fact that many archetypal QIMs are in fact integrable presents an enticing opportunity to enhance our understanding of these systems. We take a step towards this by expanding the framework of GHD to incorporate integrable interacting QIMs. We present a set of Bethe-Boltzmann type equations which incorporate the effects of impurity scattering and discuss the new aspects which include entropy production. These impurity GHD equations are then used to study a bipartioning quench wherein a relevant backscattering impurity is included at the location of the bipartition. The density and current profiles are studied as a function of the impurity strength and expressions for the entanglement entropy and full counting statistics are derived., Comment: 4.5+9 pages, 2 figures

The prediction and subsequent discovery of topological semimetal phases of matter in solid state systems has instigated a surge of activity investigating the exotic properties of these unusual materials. Amongst these are transport signatures which can be attributed to the chiral anomaly; the breaking of classical chiral symmetry in a quantum theory. This remarkable quantum phenomenon, first discovered in the context of particle physics has now found new life in condensed matter physics, connecting topological quantum matter and band theory with effective field theoretic models. In this paper we investigate the interplay between interactions and the chiral anomaly in field theories inspired by semimetals using Fujikawa's path integral method. Starting from models in one spatial dimension we discuss how the presence of interactions can affect the consequences of the chiral anomaly leading to renormalization of excitations and their transport properties. This is then generalised to the three dimensional case where we show that the anomalous response of the system, namely the chiral magnetic and quantum hall effects, are modified by the presence of interactions. These properties are investigated further through the identification of anomalous modes which exist within interacting Weyl semimetals. These massive excitations are nonperturbative in nature and are a direct consequence of the chiral anomaly. The effects of interactions on mixed axial-gravitational anomalies are then investigated and the conditions required for interactions effects to be observed are discussed., Comment: 47 pages, 1 figure

Due to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution - or its Fourier transform known as full counting statistics (FCS) - contains much more information than say the mean value of the measured observable and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the FCS is the limit of an even more general family of observables - the charged moments - that characterise how quantum entanglement is split in different symmetry sectors in the presence of a global symmetry. Here we consider the evolution of the FCS and of the charged moments of a U(1) charge truncated to a finite region after a global quantum quench. For large scales these quantities take a simple large-deviation form, showing two different regimes as functions of time: while for times much larger than the size of the region they approach a stationary value set by the local equilibrium state, for times shorter than region size they show a non-trivial dependence on time. We show that, whenever the initial state is also U(1) symmetric, the leading order in time of FCS and charged moments in the out-of-equilibrium regime can be determined by means of a space-time duality. Namely, it coincides with the stationary value in the system where the roles of time and space are exchanged. We use this observation to find some general properties of FCS and charged moments out-of-equilibrium, and to derive an exact expression for these quantities in interacting integrable models. We test this expression against exact results in the Rule 54 quantum cellular automaton and exact numerics in the XXZ spin-1/2 chain., Comment: 7+12 pages, 3+5 figures; v2 references added; v3 presentation improved, as appears in PRL

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly-bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average inter-particle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the Quench Action approach. We provide an experimentally-accessible characterisation of the stationary state by computing local pair correlation function as well as the quasi-particle distribution functions. We find that the steady state is increasingly dominated by two particle spin singlet bound states for stronger interaction strength but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power law decay suggesting a violation of Tan's contact relations., Comment: 5 pages, 2 figures

We study the quench dynamics of the one-dimensional Hubbard model through the Quench Action formalism. We introduce a class of integrable initial states -- expressed as product states over two sites -- for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between our states and the Bethe ansatz eigenstates, which we check explicitly in the limits of low densities and infinite repulsion. Our solution gives access to the stationary values attained by local observables (we show the explicit example of the density of doubly occupied sites) and the asymptotic entanglement dynamics directly in the thermodynamic limit. Interestingly, we find that for intermediate interaction strength R\'enyi entropies display a double-slope structure., Comment: 28 pages, 5 figures

We re-examine the problem of a magnetic impurity coupled to a superconductor focusing on the role of quantum fluctuations. We study in detail, a system that consists of a one-dimensional charge conserving spin-singlet superconductor coupled to a boundary magnetic impurity. Our main finding is that quantum fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intra-gap bound-states in all but a narrow region of the phase diagram. We carry out our analysis in three stages, increasing the role of the quantum fluctuations at each stage. First we consider the limit of a classical impurity and study the bulk semiclassically, finding YSR states throughout the phase diagram, a situation similar to conventional BCS superconductors. In the second stage, we reintroduce quantum fluctuations in the bulk and find that the YSR state is suppressed over half of the phase diagram, existing only around the quantum critical point separating the unscreened and the partially screened phases. In the final stage we solve exactly the full interacting model with arbitrary coupling constants using Bethe Ansatz. We find that including both the quantum fluctuating bulk and quantum impurity destabilizes the YSR state over most of the phase diagram allowing it to exist only in a small region, the YSR regime, between a Kondo-screened and an unscreened regime. Within the YSR regime a first order phase transition occurs between a spin singlet and doublet ground state. We also find that for large enough impurity spin exchange interaction a renormalized Kondo-screened regime is established. In this regime, not found for BCS superconductors, there is no YSR state and a renormalized Kondo temperature scale is generated.

Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires the use of non-perturbative techniques which are few in number, especially in high dimensions. Motivated by this we study a model of Dirac fermions in $3+1$ dimensions coupled to an arbitrary array of spins via a generalization of functional non-Abelian bosonization. We show that there exists an exact transformation of the fermions which allows us to write the system as decoupled free fermions and interacting spins. This decoupling transformation consists of a local chiral, Weyl and Lorentz transformation parameterized by solutions to a set of nonlinear differential equations which order by order takes the form of Maxwell's equations with the spins acting as sources. Owing to its chiral and Weyl components this transformation is anomalous and generates a contribution to the action. From this we obtain the effective action for the spins and expressions for the anomalous transport in the system. In the former we find that the coupling to the fermions generates kinetic terms for the spins, a long ranged interaction and a Wess-Zumino like term. In the latter we find generalizations of the chiral magnetic and Hall effects., Comment: 6 pages

Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical quantum phase transitions [DQPTs], are a recently introduced attempt to classify the myriad of possible phenomena which can occur in far from equilibrium closed quantum systems. In this work, we analytically investigate the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$ fermionic superfluids. We find that the presence of non-analyticities in the echo is not invariant under global rotations of the superfluid phase. We remedy this deficiency by introducing a more general notion of a grand canonical Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator for the long time dynamics of an interacting system. In particular, there are no DQPTs to tell apart distinct dynamical phases of quenched BCS superconductors. Nevertheless, they can signal a quench induced change in the topology and also keep track of solitons emerging from unstable stationary states of a BCS superconductor., Comment: 24 pages, 12 figures

The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one dimensional systems. In this paper we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa's path integral method we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the non-linear response of the system. In particular we find an interaction dependent density response due to a change in the magnetic field as well as a contribution to the non-equilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value., Comment: 4.5 pages

The Peierls instability toward a charge density wave is a canonical example of phonon-driven strongly correlated physics and is intimately related to topological quantum matter and exotic superconductivity. We propose a method to realize an analogous photon-mediated Peierls transition, using a system of one-dimensional tubes of interacting Bose or Fermi atoms trapped inside a multimode confocal cavity. Pumping the cavity transversely engineers a cavity-mediated metal--to--insulator transition in the atomic system. For strongly interacting bosons in the Tonks-Girardeau limit, this transition can be understood (through fermionization) as being the Peierls instability. We extend the calculation to finite values of the interaction strength and derive analytic expressions for both the cavity field and mass gap. They display nontrivial power law dependence on the dimensionless matter-light coupling., Comment: 6 pages, 2 figures; supplement of 4 pages; published version

Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur., Comment: This version is superseded by an expanded and corrected manuscript by Rylands, Yuzbashyan, Guarie, Zabalo & Galitski arXiv:2103.03754

The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can support Majorana bound states which play a crucial role in the realm of quantum computation. In this work we examine the boundary modes in an interacting quantum wire with a proximity induced pairing term. We solve the system exactly by Bethe Ansatz and show that for certain boundary conditions the spectrum contains bound states localized about either edge. The model is shown to exhibit a first order phase transition as a function of the interaction strength such that for attractive interactions the ground state has bound states at both ends of the wire while for repulsive interactions they are absent. In addition we see that the bound state energy lies within the gap for all values of the interaction strength but undergoes a sharp avoided level crossing for sufficiently strong interaction, thereby preventing its decay. This avoided crossing is shown to occur as a consequence of an exact self-duality which is present in the model., Comment: 6 pages

Quantum impurity models are prevalent throughout many body physics, providing some prime examples of strongly correlated systems. Aside from being of great interest in themselves they can provide deep insight into the effects of strong correlations in general. The classic example is the Kondo model wherein a magnetic impurity is screened at low energies by a non interacting metallic bath. Here we consider a magnetic impurity coupled to a quantum wire with pairing interaction which dynamically generates a mass gap. Using Bethe Ansatz we solve the system exactly finding that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground state density of states and magnetization in both phases as well as the excitations. In contrast to the well studied case of magnetic impurities in superconductors we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but with quantum fluctuations., Comment: 4+10 pages, 1 figure

The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in the angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Linger model, the dynamical localization can persist., Comment: 5 pages, 2 figures

Driven by breakthroughs in experimental and theoretical techniques, the study of non-equilibrium quantum physics is a rapidly expanding field with many exciting new developments. Amongst the manifold ways the topic can be investigated, one dimensional system provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques and experimental viability have resulted in a flurry of research activity over the last decade or so. In this review we explore the non equilibrium aspects of one dimensional systems which are integrable. Through a number of illustrative examples we discuss non equilibrium phenomena which arise in such models, the role played by integrability and the consequences these have for more generic systems., Comment: 31 pages, 10 Figures. To be published in Annual Reviews of Condensed Matter Physics

A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench., Comment: 7 pages, 2 figures

The Sine-Gordon - equivalently, the massive Thirring - Hamiltonian is ubiquitous in low-dimensional physics, with applications that range from cold atom and strongly correlated systems to quantum impurities. We study here its non-equilibrium dynamics using the quantum quench protocol - following the system as it evolves under the Sine-Gordon Hamiltonian from initial Mott type states with large potential barriers. By means of the Bethe Ansatz we calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing these quenches for different values of the interaction strength. Some universal features are noted as well as an interesting duality relating quenches in different parameter regimes of the model., Comment: 14 pages plus appendices

Quantum impurity models play an important role in many areas of physics from condensed matter to AMO and quantum information. They are important models for many physical systems but also provide key insights to understanding much more complicated scenarios. In this paper we introduce a simplified method to describe the thermodynamic properties of integrable quantum impurity models. We show this method explicitly using the anisotropic Kondo and the interacting resonant level models. We derive a simplified expression for the free energy of both models in terms of a single physically transparent integral equation which is valid at all temperatures and values of the coupling constants.

A quantum impurity attached to an interacting quantum wire gives rise to an array of of new phenomena. Using Bethe Ansatz we solve exactly models describing two geometries of a quantum dot coupled to an interacting quantum wire: a quantum dot that is (i) side-coupled and (ii) embedded in a Luttinger liquid. We find the eigenstates and determine the spectrum through the Bethe Ansatz equations. Using this we derive exact expressions for the ground state dot occupation. The thermodynamics are then studied using the thermodynamics Bethe Ansatz equations. It is shown that at low energies the dot becomes fully hybridized and acts as a backscattering impurity or tunnel junction depending on the geometry and furthermore that the two geometries are related by changing the sign of the interactions. Although remaining strongly coupled for all values of the interaction in the wire, there exists competition between the tunneling and backscattering leading to a suppression or enhancement of the dot occupation depending on the sign of the bulk interactions., Comment: 13 pages, v2 expanded and more calculations added

We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling and the dot is modeled as an interacting resonant level on to which the bulk fermions can tunnel. We solve the Hamiltonian exactly and construct all eigenstates. We study both the zero and finite temperature properties of the system, in particular we compute the exact dot occupation as a function of the dot energy in all parameter regimes. The system is seen to flow from weak to to strong coupling for all values of the bulk interaction, with the flow characterized by a non-perturbative Kondo scale. We identify the critical exponents at the weak and strong coupling regimes., Comment: 9 pages + appendices Published version

A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a localised transmitting and reflecting impurity. We solve exactly the Hamiltonian by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. A related model, the Weak-Tunnelling model, wherein the impurity is replaced by a tunnel junction, is solved by the same method. The consistency of the construction is established through a generalised Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe Ansatz equations are derived by means of the Off Diagonal Bethe Ansatz approach. We derive the spectrum of the model for all coupling constant regimes and calculate the impurity free energy. We discuss the low energy behaviour of the systems for both repulsive and attractive interactions., Comment: 15 pages

The superradiant behaviour of the Dicke model is examined using the Yudson representation. This is achieved by computing the time evolution of the mean photon current density and photon number. Extensions of this model including energy splitting and spatial separation are then investigated using this technique., Comment: 7 pages, 3 Figures