# Publications by Fabian Essler

## Reduced Density Matrix after a Quantum Quench

ArXiv (0)

We consider the reduced density matrix (RDM) \rho_A(t) for a finite subsystem A after a global quantum quench in the infinite transverse-field Ising chain. It has been recently shown that the infinite time limit of \rho_A(t) is described by the RDM \rho_{GGE,A} of a generalized Gibbs ensemble. Here we present some details on how to construct this ensemble in terms of local integrals of motion, and show its equivalence to the expression in terms of mode occupation numbers widely used in the literature. We then address the question, how \rho_A(t) approaches \rho_{GGE,A} as a function of time. To that end we introduce a distance on the space of density matrices and show that it approaches zero as a universal power-law t^{-3/2} in time. As the RDM completely determines all local observables within A, this provides information on the relaxation of correlation functions of local operators. We then address the issue, of how well a truncated generalized Gibbs ensemble with a finite number of local higher conservation laws describes a given subsystem at late times. We find that taking into account only local conservation laws with a range at most comparable to the subsystem size provides a good description. However, excluding even a single one of the most local conservation laws in general completely spoils this agreement.

## Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

ArXiv (0)

We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values, that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.

## Dynamical Correlations after a Quantum Quench

ArXiv (0)

In many integrable models static (equal time) correlation functions of local observables after a quantum quench relax to stationary values, which are described by a generalized Gibbs ensemble (GGE). Here we establish that the same holds true for dynamic (non equal time) correlation functions. More generally we show that in the absence of long-range interactions in the final Hamiltonian, the dynamics is determined by the same ensemble that describes static correlations. When the latter is a GGE the basic form of the fluctuation dissipation theorem holds, although the absorption and emission spectra are not simply related as in the thermal case. For quenches in the transverse field Ising chain (TFIC) we derive explicit expressions for the time evolution of dynamic order parameter correlators after a quench.

## Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties

ArXiv (0)

We consider the stationary state properties of the reduced density matrix as well as spin-spin correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. We demonstrate that stationary state properties are described by a generalized Gibbs ensemble. We discuss the approach to the stationary state at late times.

## Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators

ArXiv (0)

We consider the time evolution of order parameter correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. Using two novel methods based on determinants and form factor sums respectively, we derive analytic expressions for the asymptotic behaviour of one and two point correlators. We discuss quenches within the ordered and disordered phases as well as quenches between the phases and to the quantum critical point. We give detailed account of both methods.

## The role of symmetries in systems of strongly correlated electrons

CORRELATION EFFECTS IN LOW-DIMENSIONAL ELECTRON SYSTEMS **118** (1994) 57-67

## Electronic model for superconductivity.

Phys Rev Lett **70** (1993) 73-76

## Higher conservation laws and algebraic Bethe Ansa-umltze for the supersymmetric t-J model.

Phys Rev B Condens Matter **46** (1992) 9147-9162

## New exactly solvable model of strongly correlated electrons motivated by high-Tc superconductivity.

Phys Rev Lett **68** (1992) 2960-2963

## COMPLETENESS OF THE SO(4) EXTENDED BETHE ANSATZ FOR THE ONE-DIMENSIONAL HUBBARD-MODEL

NUCLEAR PHYSICS B **384** (1992) 431-458

## FINE-STRUCTURE OF THE BETHE ANSATZ FOR THE SPIN-1/2 HEISENBERG X X X MODEL

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL **25** (1992) 4115-4126

## NEW EIGENSTATES OF THE 1-DIMENSIONAL HUBBARD-MODEL

NUCLEAR PHYSICS B **372** (1992) 559-596

## Complete solution of the one-dimensional Hubbard model.

Phys Rev Lett **67** (1991) 3848-3851

## Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

ArXiv (0)

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

## On thermal fluctuations in quantum magnets

Physical review B: Condensed matter and materials physics American Physical Society (0)

The effect of thermal fluctuations on the dynamics of a gapped quantum magnet is studied using inelastic neutron scattering on copper nitrate, a model material for the one-dimensional (1D) bond alternating Heisenberg chain, combined with theoretical and numerical analysis. We observe and interpret the thermally induced central peak due to intraband scattering as well as the thermal development of an asymmetric continuum of scattering. We relate this asymmetric line broadening to hard core constraints and quasi-particle interactions. Our findings are a counter example to recent assertions of universality of line broadening in 1D systems and are to be considered as a new paradigm of behaviour, applicable to a broad range of quantum systems.

## Exactly Solvable Models of Strongly Correlated Electrons

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This is a reprint volume devoted to exact solutions of models of strongly correlated electrons in one spatial dimension by means of the Bethe Ansatz.

## Higher conservation laws and algebraic Bethe Ansätze for the supersymmetric t-J model

Physical Review B: Condensed Matter and Materials Physics American Physical Society (0)

We construct the enveloping fundamental spin model of the t-J hamiltonian using the Quantum Inverse Scattering Method (QISM), and present all three possible Algebraic Bethe Ans\"atze. Two of the solutions have been previously obtained in the framework of Coordinate Space Bethe Ansatz by Sutherland and by Schlottmann and Lai, whereas the third solution is new. The formulation of the model in terms of the QISM enables us to derive explicit expressions for higher conservation laws.