arXiv subjects

Colin Rylands

Publications and source records attributed to Colin Rylands.

At least 19 recordsLinked to original sources

arXiv2026

Boundary quenches in (1+1)-dimensional conformal field theory

We investigate a class of local quantum quenches in which the conformal boundary condition of a (1+1)-dimensional conformal field theory is abruptly changed. We derive a remarkably simple and universal expression for the time evolution of one-point functions on the half-line. This result provides a direct description of the propagation of the disturbance generated by the quench and, in turn, allows us to determine the dynamics of bipartite entanglement for subsystems adjacent to the boundary. We show that, once the subsystem becomes fully causally connected to the quench event, the entanglement entropy undergoes a sharp finite jump whose magnitude is universally given by the logarithm of the ratio of the boundary g-factors associated with the initial and final boundary conditions. We benchmark these analytical predictions against Matrix Product State simulations of the critical Ising spin chain, finding excellent agreement. The numerical analysis further allows us to investigate the time evolution of the spin-flip entanglement asymmetry, revealing how the symmetry-breaking perturbation emitted from the boundary propagates through the system. Our results uncover universal dynamical signatures of boundary quenches and establish a direct connection between nonequilibrium entanglement dynamics and boundary critical phenomena.

cond-mat.stat-mech↗

arXiv2026

Asymmetry dynamics and nonequilibrium symmetry-breaking phase transitions

In classical settings, the Mpemba effect occurs when a hotter system cools faster than an initially colder one. In quantum systems, this effect can be reinterpreted exploiting the concept of symmetries, with the asymmetry of a subsystem playing the role of temperature. A quantum Mpemba effect arises when a more asymmetric state restores the symmetry faster than a less asymmetric one. Previous work mainly focuses on closed systems characterized by thermal equilibration and Hamiltonian symmetries. In this paper, we analyze the dynamics of asymmetry in an open quantum many-body system featuring symmetry breaking and uncover dynamical behavior that appears to be unique to these settings. In the symmetric phase, we demonstrate the existence of a quantum Mpemba effect, which emerges as a direct consequence of a non-monotonic evolution of the asymmetry. In the broken-symmetry phase, we analyze the imbalance between the system's ability to increase or to decrease its asymmetry. Our results extend the notion of quantum Mpemba effects to open quantum many-body systems exhibiting symmetry-breaking phase transitions and establish them as a platform for observing and controlling anomalous relaxation phenomena.

cond-mat.stat-mech↗

arXiv2026

Initial State Memory in Finite Random Brickwork Circuits

We ask under what conditions a finite brickwork circuit of random gates retains local information about the initial state. To answer this question we measure the averaged Frobenius distance between the reduced states obtained by evolving two arbitrary initial states and tracing out a portion of the system. By characterising this distance exactly at all times we find that the information is retained if the environment -- the subsystem traced out -- is smaller than half of the system and washed away otherwise. We also find that, while the dynamics of the Frobenius distance depends on the specific initial states chosen, this dependence becomes increasingly weak for large scales and eventually the Frobenius distance attains a universal form as a function of time. Finally, we show that by introducing weak enough boundary dissipation, one can observe a phase transition between a memory preserving phase and one where the information is completely lost.

quant-ph↗

arXiv2025

Entanglement evolution from entangled multipodal states

In a periodic lattice system an entangled antipodal pair state, otherwise known as a crosscap state, is a simple two site product state in which spins at antipodal sites are prepared in Bell pairs. Such states have maximal bipartite entanglement and serve as a useful platform for studying the quench dynamics of systems which have large initial entanglement. In this paper, we study a generalization of these states which we dub entangled mutipodal states. These states, which are defined for fermionic systems, generalize the crosscap states by having correlations among more than two sites, specifically, those which sit at the vertices of regular polygons. By construction, the states are Gaussian and translationally invariant allowing many of their properties to be understood. We study the bipartite entanglement entropy of these states both in and out of equilibrium. In equilibrium, the entanglement profile as a function of subsystem size exhibits two distinct regimes, a volume-law growth followed by a saturation to a constant value, thus generalizing the Page-curve profile of the crosscap state. In the non-equilibrium setting, we study quenches from these initial states to the free-fermion chain, whose ensuing dynamics displays a far richer structure compared to the crosscap case. We interpret our results in terms of the quasiparticle picture, which requires multiplets of quasiparticles to be excited non-locally around the system. This scenario is confirmed by the appearance of a post-quench, negative tripartite information.

cond-mat.stat-mech↗

arXiv2025

Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case

We consider the effect of projective measurements on the quench dynamics of the bipartite entanglement entropy in one dimensional free fermionic systems. In our protocol, we consider projective measurements of a $U(1)$ conserved charge, the particle number, on some large subsystem, and study the entanglement entropies between the same subsystem and its complement. We compare the dynamics emanating from two classes of initial states, one which is an eigenstate of the charge and another which is not. Moreover, we consider the effects of a single measurement as well as multiple which are periodically performed. Using the quasiparticle picture, we obtain analytic expressions for the behaviour of the entanglement which admit a transparent physical interpretation. In general, we find that measurements introduce two distinct types of corrections to the entanglement, which can be interpreted separately as classical and quantum contributions. The classical contribution is independent of the measurement outcome and scales logarithmically with variance of the charge distribution. In contrast, the quantum contribution depends on the specific measurement outcome and can be significant for individual realizations; however, it becomes negligible when averaged over all possible outcomes. Our expressions reduce to previously known results for symmetry resolved entanglement and full counting statistics in some relevant limits, and are confirmed by an exact calculation performed on the N\'eel initial state.

quant-ph↗

arXiv2025

A simpler probe of the quantum Mpemba effect in closed systems

We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy can be very well approximated by an entropy difference, affording a significant computational advantage. We go on to relate this to the entanglement asymmetry of the subsystem with respect to time translation invariance. In doing this, we obtain a simple probe of the relaxation dynamics of closed many-body systems and use it to re-examine the quantum Mpemba effect, wherein states can relax faster if they are initially further from equilibrium. We reproduce earlier instances of the effect related to symmetry restoration as well as uncover new cases in the absence of such symmetries. For integrable models, we obtain the criteria for this to occur using the quasiparticle picture. Lastly, we show that, in models obeying the entanglement membrane picture, the quantum Mpemba effect cannot occur for a large class of initial states.

cond-mat.stat-mech↗

arXiv2025

Quench dynamics of negativity Hamiltonians

In this paper, we investigate the quench dynamics of the negativity and fermionic negativity Hamiltonians in free fermionic systems. We do this by generalizing a recently developed quasiparticle picture for the entanglement Hamiltonians to tripartite geometries. We obtain analytic expressions for these quantities which are then extensively checked against previous results and numerics. In particular, we find that the standard negativity Hamiltonian contains both non-local hopping terms and four fermion interactions, whereas the fermionic version is purely quadratic. However, despite their marked difference, we show that the logarithmic negativity obtained from either are identical in the ballistic scaling limit, as are their symmetry resolution.

quant-ph↗

arXiv2025

Emergent boundary supersymmetry in a one dimensional superconductor

The interplay between bulk properties and boundary conditions in one-dimensional quantum systems, gives rise to many intriguing phenomena. These include the emergence of zero energy modes which are of significant interest to a variety of fields. In this work we investigate the presence of such zero modes in cases where the boundary conditions are dynamical and arise due to the coupling to some quantum degrees of freedom. In particular, we study a one-dimensional spin-singlet superconductor, modeled by the Gross-Neveu field theory, coupled to spin $\frac{1}{2}$ magnetic impurities at its boundaries via a spin-exchange interaction. We solve the model exactly for arbitrary values of the bulk and the impurity coupling strengths using nested coordinate Bethe ansatz and show that the system exhibits a rich boundary phase structure. For a range of couplings, the low energy degrees of freedom form irreducible representations of the supersymmetric $spl(2,1)\otimes spl(2,1)$ algebra which become degenerate at a specific point, indicating the emergence of supersymmetry in the low energy boundary degrees of freedom. We show that at the supersymmetric point there exist exact zero energy modes that map one ground state with the other. We express these in terms of the generators of the algebra.

cond-mat.str-el↗

arXiv2024

Quench dynamics of entanglement from crosscap states

The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics. It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments. The entanglement dynamics emerging from long-range correlated states is far less studied, although no less viable using modern quantum simulation experiments. In this work, we investigate the dynamics of the bipartite entanglement entropy and mutual information from initial states which have long-range entanglement with correlation between antipodal points of a finite and periodic system. Starting from these crosscap states, we study both brickwork quantum circuits and Hamiltonian dynamics and find distinct patterns of behaviour depending on the type of dynamics and whether the system is integrable or chaotic. Specifically, we study both dual unitary and random unitary quantum circuits as well as free and interacting fermion Hamiltonians. For integrable systems, we find that after a time delay the entanglement experiences a linear in time decrease followed by a series of revivals, while, in contrast, chaotic systems exhibit constant entanglement entropy. On the other hand, both types of systems experience an immediate linear decrease of the mutual information in time. In chaotic systems this then vanishes, whereas integrable systems instead experience a series of revivals. We show how the quasiparticle and membrane pictures of entanglement dynamics can be modified to describe this behaviour, and derive explicitly the quasiparticle picture in the case of free fermion models which we then extend to all integrable systems.

cond-mat.stat-mech↗

arXiv2024

Quasiparticle Picture for Entanglement Hamiltonians in Higher Dimensions

We employ the quasiparticle picture of entanglement evolution to obtain an effective description for the out-of-equilibrium Entanglement Hamiltonian at the hydrodynamical scale following quantum quenches in free fermionic systems in two or more spatial dimensions. Specifically, we begin by applying dimensional reduction techniques in cases where the geometry permits, building directly on established results from one-dimensional systems. Subsequently, we generalize the analysis to encompass a wider range of geometries. We obtain analytical expressions for the entanglement Hamiltonian valid at the ballistic scale, which reproduce the known quasiparticle picture predictions for the Renyi entropies and full counting statistics. We also numerically validate the results with excellent precision by considering quantum quenches from several initial configurations.

cond-mat.stat-mech↗

arXiv2024

Entanglement asymmetry in CFT with boundary symmetry breaking

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.

hep-th↗

arXiv2024

Entanglement in dual unitary quantum circuits with impurities

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, shedding light on the range of validity of the membrane picture in such systems.

cond-mat.stat-mech↗

arXiv2024

Dynamical symmetry restoration in the Heisenberg spin chain

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.

cond-mat.stat-mech↗

arXiv2024

Entanglement Hamiltonians and the quasiparticle picture

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 analytic result for the EH following a quantum quench in non-interacting fermionic models, valid in the ballistic scaling regime. The derivation adapts the celebrated quasiparticle picture to operators, providing detailed insights into its physical properties. The resulting analytic formula serves as a foundation for engineering EHs in quantum optics experiments.

quant-ph↗

arXiv2024

Translation symmetry restoration under random unitary dynamics

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, where our method leads to exact results. We show that 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. We provide the first exact characterisation of this effect in a non-integrable system.

cond-mat.stat-mech↗

arXiv2024

Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect

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.

cond-mat.stat-mech↗

arXiv2023

Full Counting Statistics of Charge in Quenched Quantum Gases

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.

cond-mat.stat-mech↗

arXiv2023

Microscopic origin of the quantum Mpemba effect in integrable systems

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.

cond-mat.stat-mech↗