# Publications by Fabian Essler

## Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2019) ARTN 084012

YD van Nieuwkerk, FHL Essler

## Almost strong (0, pi) edge modes in clean interacting one-dimensional Floquet systems

PHYSICAL REVIEW B 99 (2019) ARTN 205419

DJ Yates, FHL Essler, A Mitrai

## NMR relaxation in Ising spin chains

PHYSICAL REVIEW B 99 (2019) ARTN 035156

J Steinberg, NP Armitage, FHL Essler, S Sachdev

## Full counting statistics in the transverse field Ising chain

SCIPOST PHYSICS 4 (2018) ARTN 043

S Groha, F Essler, P Calabrese

## Finite-temperature dynamics of the Mott insulating Hubbard chain

PHYSICAL REVIEW B 97 (2018) ARTN 045146

A Nocera, FHL Essler, AE Feiguin

## Critical behavior of the extended Hubbard model with bond dimerization

PHYSICA B-CONDENSED MATTER 536 (2018) 474-478

S Ejima, F Lange, FHL Essler, H Fehske

## Integrable spin chains with random interactions

PHYSICAL REVIEW B 98 (2018) ARTN 024203

FHL Essler, IR van den Berg, V Gritsev

## Projective phase measurements in one-dimensional Bose gases

SciPost Physics Stichting SciPost 5 (2018) 046

YD van Nieuwkerk, J Schmiedmayer, F Essler

<jats:p>We consider time-of-flight measurements in split one-dimensional Bose gases. It is well known that the low-energy sector of such systems can be described in terms of two compact phase fields <jats:inline-formula><jats:alternatives><jats:tex-math>\hat{\phi}_{a,s}(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mover><mml:mi>ϕ</mml:mi><mml:mo accent="true">̂</mml:mo></mml:mover><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. Building on existing results in the literature we discuss how a single projective measurement of the particle density after trap release is in a certain limit related to the eigenvalues of the vertex operator <jats:inline-formula><jats:alternatives><jats:tex-math>e^{i\hat{\phi}_a(x)}</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:msub><mml:mover><mml:mi>ϕ</mml:mi><mml:mo accent="true">̂</mml:mo></mml:mover><mml:mi>a</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:msup></mml:math></jats:alternatives></jats:inline-formula>. We emphasize the theoretical assumptions underlying the analysis of “single-shot” interference patterns and show that such measurements give direct access to multi-point correlation functions of <jats:inline-formula><jats:alternatives><jats:tex-math>e^{i\hat{\phi}_a(x)}</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:msub><mml:mover><mml:mi>ϕ</mml:mi><mml:mo accent="true">̂</mml:mo></mml:mover><mml:mi>a</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:msup></mml:math></jats:alternatives></jats:inline-formula> in a substantial parameter regime. For experimentally relevant situations, we derive an expression for the measured particle density after trap release in terms of convolutions of the eigenvalues of vertex operators involving both sectors of the two-component Luttinger liquid that describes the low-energy regime of the split condensate. This opens the door to accessing properties of the symmetric sector via an appropriate analysis of existing experimental data.</jats:p>

## Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy

SciPost Physics Stichting SciPost 5 (2018) 059

S Ejima, T Yamaguchi, F Essler, F Lange, Y Ohta, H Fehske

<jats:p>We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.</jats:p>

## Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50 (2017) ARTN 334002

S Groha, FHL Essler

## On truncated generalized Gibbs ensembles in the Ising field theory

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2017) ARTN 013103

FHL Essler, G Mussardo, M Panfil

## Full counting statistics in the spin-1/2 Heisenberg XXZ chain

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50 (2017) ARTN 414002

M Collura, FHL Essler, S Groha

## Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet

PHYSICAL REVIEW B 96 (2017) ARTN 054423

AK Bera, B Lake, FHL Essler, L Vanderstraeten, C Hubig, U Schollwoeck, ATMN Islam, A Schneidewind, DL Quintero-Castro

## Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 375 (2017)

T Veness, FHL Essler, MPA Fisher

We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014 J. Stat. Mech.2014, P10010. (doi:10.1088/1742-5468/2014/10/P10010)). These states are atypical in the sense that their entropy density is smaller than that of thermal states at the same energy density. Furthermore, we show that thermal states in a particular temperature window exhibit a weaker form of the QDL property, in agreement with recent results obtained by strong-coupling expansion methods in Veness et al. (2016 (http://arxiv.org/abs/1611.02075)).This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

## Quantum disentangled liquid in the half-filled Hubbard model

PHYSICAL REVIEW B 96 (2017) ARTN 195153

T Veness, FHL Essler, MPA Fisher

## Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise.

Physical review letters 117 (2016) 137202-

MV Medvedyeva, FHL Essler, T Prosen

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

## Thermalization and light cones in a model with weak integrability breaking

PHYSICAL REVIEW B 94 (2016) ARTN 245117

B Bertini, FHL Essler, S Groha, NJ Robinson

## Introduction to 'Quantum Integrability in Out of Equilibrium Systems'

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016) ARTN 064001

P Calabrese, FHL Essler, G Mussardo

## Quench dynamics and relaxation in isolated integrable quantum spin chains

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016) ARTN 064002

FHL Essler, M Fagotti

## Ising tricriticality in the extended Hubbard model with bond dimerization

PHYSICAL REVIEW B 93 (2016) ARTN 235118

S Ejima, FHL Essler, F Lange, H Fehske