Emanuele Levi

Entanglement entropy of non-unitary conformal field theory

Here we show that the Renyi entanglement entropy of a region of large size l in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as ceff(n+1)/2n log(L), where ceff=c-24Delta > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Delta < 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic, then there is an additional term proportional to

Robustness of many-body localization in the presence of dissipation

log(log(L)). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

Dynamics of many-body localization in a translation-invariant quantum glass model

Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.

Non-equilibrium universality in the dynamics of dissipative cold atomic gases

We study the real-time dynamics of a translationally invariant quantum spin chain, based on the East kinetically constrained glass model, in search for evidence of many-body localisation in the absence of disorder. Numerical simulations indicate a change, controlled by a coupling parameter, from a regime of fast relaxation---corresponding to thermalisation---to a regime of very slow relaxation. This slowly relaxing regime is characterised by dynamical features usually associated with non-ergodicity and many-body localisation (MBL): memory of initial conditions, logarithmic growth of entanglement entropy, and non-exponential decay of time-correlators. We show that slow relaxation is a consequence of sensitivity to spatial fluctuations in the initial state. While numerics indicate that certain relaxation timescales grow markedly with size, our finite size results are consistent both with an MBL transition, expected to only occur in disordered systems, or with a pronounced quasi-MBL crossover.

Role of interactions in a dissipative many-body localized system

The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established concept at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decades it has been challenging to find experimental systems that manifest this transition. Here we show theoretically that signatures of the directed percolation universality class can be observed in an atomic system with long range interactions. Moreover, we demonstrate that even mesoscopic ensembles — which are currently studied experimentally — are sufficient to observe traces of this non-equilibrium phase transition in one, two and three dimensions.

Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder

Recent experimental and theoretical efforts have focused on the effect of dissipation on quantum many-body systems in their many-body localized (MBL) phase. While in the presence of dephasing noise such systems reach a unique ergodic state, their dynamics is characterized by slow relaxation manifested in nonexponential decay of self-correlations. Here we shed light on a currently much debated issue, namely, the role of interactions for this relaxation dynamics. We focus on the experimentally relevant situation of the evolution from an initial charge density wave in the presence of strong dephasing noise. We find a crossover from a regime dominated by disorder to a regime dominated by interactions, with an accompanying change of time correlators from stretched exponential to compressed exponential form. The strongly interacting regime can be explained in terms of nucleation and growth dynamics of relaxing regions—reminiscent of the kinetics of crystallization in soft matter systems—and should be observable experimentally. This interaction-driven crossover suggests that the competition between interactions and noise gives rise to a much richer structure of the MBL phase than anticipated so far.

Crystalline structures and frustration in a two-component Rydberg gas

We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.Disordered systems provide paradigmatic instances of ergodicity breaking and localization phenomena. Here we explore the dynamics of excitations in a system of Rydberg atoms held in optical tweezers. The finite temperature produces an intrinsic uncertainty in the atomic positions, which translates into quenched correlated disorder in the interatomic interaction strengths. In a simple approach, the dynamics in the many-body Hilbert space can be understood in terms of a one-dimensional Anderson-like model with disorder on every other site, featuring both localized and delocalized states. We conduct an experiment on an eight-atom chain and observe a clear suppression of excitation transfer. Our experiment accesses a regime which is described by a twodimensional Anderson model on a “trimmed” square lattice. Our results thus provide a concrete example in which the absence of excitation propagation in a many-body system is directly related to Anderson-like localization in the Hilbert space, which is believed to be the mechanism underlying many-body localization.

Higher particle form factors of branch point twist fields in integrable quantum field theories

We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of compatible to incompatible transitions. The incompatibility between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar–Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.

Arguments towards a c-theorem from branch-point twist fields

In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive (1+1)-dimensional integrable quantum field theories and their correlation functions are related to the bi-partite entanglement entropy. We find analytic expressions for some form factors and check those expressions for consistency, mainly by evaluating the conformal dimension of the corresponding twist field in the underlying conformal field theory. We find that solutions to the form factor equations are not unique so various techniques need to be used to identify those corresponding to the branch point twist field we are interested in. The models for which we carry out our study are characterized by staircase patterns of various physical quantities as functions of the energy scale. As the latter is varied, the β-function associated with these theories comes close to vanishing at several points between the deep infrared and deep ultraviolet regimes. In other words, renormalization group flows approach the vicinity of various critical points before ultimately reaching the ultraviolet fixed point. This feature provides an optimal way of checking the consistency of higher particle form factor solutions, as the changes on the conformal dimension of the twist field at various energy scales can only be accounted for by considering higher particle form factor contributions to the expansion of certain correlation functions.

Non-classical correlations in a class of spin chains with long-range interactions and exactly solvable ground states

A fundamental quantity in (1+1)-dimensional quantum field theories is Zamolodchikovs c-function. A function of a renormalization group distance parameter r, which interpolates between ultraviolet and infrared fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points (r = 0 and r = ∞). At those points, c(r) becomes the central charge of the conformal field theory which describes the critical point. In this communication, we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function , which involves the branch-point twist field and the trace of the stress–energy tensor Θ, has exactly the same qualitative features as c(r).