arXiv subjects

Fabian H. L. Essler

Publications and source records attributed to Fabian H. L. Essler.

At least 73 records · Page 4Linked to original sources

arXiv2014

Quantum quench in the sine-Gordon model

We consider the time evolution in the repulsive sine-Gordon quantum field theory after the system is prepared in a particular class of initial states. We focus on the time dependence of the one-point function of the semi-local operator $\exp\big(i\ β\ Φ(x)/2\big)$. By using two different methods based on form-factor expansions, we show that this expectation value decays to zero exponentially, and we determine the decay rate by analytical means. Our methods generalise to other correlation functions and integrable models.

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arXiv2014

"Quasi-particle breakdown" in the quasi-one-dimensional Ising ferromagnet CoNb$_2$O$_6$

We present experimental and theoretical evidence that an interesting quantum many-body effect -- quasi-particle breakdown -- occurs in the quasi-one-dimensional spin-1/2 Ising-like ferromagnet CoNb$_2$O$_6$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of CoNb$_2$O$_6$ and determine the exchange parameters of this model by fitting the calculated single particle dispersion to the one observed experimentally in applied transverse magnetic fields. We present high-resolution inelastic neutron scattering measurements of the single particle dispersion which observe "anomalous broadening" effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for non-zero matrix elements for decay by breaking the $\mathbb{Z}_2$ spin inversion symmetry of the Hamiltonian.

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arXiv2014

"Light-cone" dynamics after quantum quenches in spin chains

Signal propagation in the non equilibirum evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.

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arXiv2014

Entanglement Entropies of the quarter filled Hubbard model

We study Renyi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We show that these can be understood in terms of a "shell-filling" effect, and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalisation group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically, and we present an effective way to take them into account.

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arXiv2014

Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain

We consider the time evolution after quantum quenches in the spin-1/2 Heisenberg XXZ quantum spin chain with Ising-like anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including Néel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.

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arXiv2013

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

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.

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arXiv2013

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

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.

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arXiv2013

Reduced Density Matrix after a Quantum Quench

We consider the reduced density matrix (RDM) ρ_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 ρ_A(t) is described by the RDM ρ_{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 ρ_A(t) approaches ρ_{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.

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arXiv2013

Time evolution of local observables after quenching to an integrable model

We consider quantum quenches in integrable models. We argue that the behaviour of local observables at late times after the quench is given by their expectation values with respect to a single representative Hamiltonian eigenstate. This can be viewed as a generalization of the eigenstate thermalization hypothesis to quantum integrable models. We present a method for constructing this representative state by means of a generalized Thermodynamic Bethe Ansatz (GTBA). Going further, we introduce a framework for calculating the time dependence of local observables as they evolve towards their stationary values. As an explicit example we consider quantum quenches in the transverse-field Ising chain and show that previously derived results are recovered efficiently within our framework.

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arXiv2012

Dynamical Correlations after a Quantum Quench

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.

cond-mat.stat-mech↗

arXiv2012

Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions

We consider the von Neumann and Rényi entropies of the one dimensional quarter-filled Hubbard model. We observe that for periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We explain this observation in terms of a shell-filling effect, and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems.

cond-mat.str-el↗

arXiv2012

Dynamics in the Ising field theory after a quantum quench

We study the real-time dynamics of the order parameter $<σ(t)>$ in the Ising field theory after a quench in the fermion mass, which corresponds to a quench in the transverse field of the corresponding transverse field Ising chain. We focus on quenches within the ordered phase. The long-time behaviour is obtained analytically by a resummation of the leading divergent terms in a form-factor expansion for $<σ(t)>$. Our main result is the development of a method for treating divergences associated with working directly in the field theory limit. We recover the scaling limit of the corresponding result by Calabrese et al. [Phys. Rev. Lett. \textbf{106}, 227203 (2011)], which was obtained for the lattice model. Our formalism generalizes to integrable quantum quenches in other integrable models.

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arXiv2011

Observing complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches

We consider the non-equilibrium evolution in the spin-1/2 XXZ Heisenberg chain for fixed magnetization after a local quantum quench. This model is equivalent to interacting spinless fermions. Initially an infinite magnetic field is applied to n consecutive sites and the ground state is calculated. At time t=0 the field is switched off and the time evolution of observables such as the z-component of spin is computed using the Time Evolving Block Decimation (TEBD) algorithm. We find that the observables exhibit strong signatures of linearly propagating spinon and bound state excitations. These persist even when integrability-breaking perturbations are included. Since bound states ("strings") are notoriously difficult to observe using conventional probes such as inelastic neutron scattering, we conclude that local quantum quenches are an ideal setting for studying their properties. We comment on implications of our results for cold atom experiments.

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arXiv2011

Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states

We determine the local density of states (LDOS) for spin-gapped one-dimensional charge density wave (CDW) states and Mott insulators in the presence of a hard-wall boundary. We calculate the boundary contribution to the single-particle Green function in the low-energy limit using field theory techniques and analyze it in terms of its Fourier transform in both time and space. The boundary LDOS in the CDW case exhibits a singularity at momentum 2kF, which is indicative of the pinning of the CDW order at the impurity. We further observe several dispersing features at frequencies above the spin gap, which provide a characteristic signature of spin-charge separation. This demonstrates that the boundary LDOS can be used to infer properties of the underlying bulk system. In presence of a boundary magnetic field mid-gap states localized at the boundary emerge. We investigate the signature of such bound states in the LDOS. We discuss implications of our results on STM experiments on quasi-1D systems such as two-leg ladder materials like Sr14Cu24O41. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of one-dimensional Mott insulators.

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arXiv2011

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field

We investigate the properties of the Heisenberg S=1 chain with bilinear and biquadratic interactions in a magnetic field using the Density Matrix Renormalization Group, Bethe ansatz and field theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This liquid undergoes a continuous pair unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector chiral phase.

cond-mat.str-el↗

arXiv2011

Quantum Quench in the Transverse Field Ising Chain

We consider the time evolution of observables in the transverse field Ising chain (TFIC) after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.

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arXiv2011

Current large deviation function for the open asymmetric simple exclusion process

We consider the one dimensional asymmetric exclusion process with particle injection and extraction at two boundaries. The model is known to exhibit four distinct phases in its stationary state. We analyze the current statistics at the first site in the low and high density phases. In the limit of infinite system size, we conjecture an exact expression for the current large deviation function.

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arXiv2010

Universal corrections to scaling for block entanglement in spin-1/2 XX chains

We consider the Rényi entropies $S_n(\ell)$ in the one dimensional spin-1/2 Heisenberg XX chain in a magnetic field. The case n=1 corresponds to the von Neumann ``entanglement'' entropy. Using a combination of methods based on the generalized Fisher-Hartwig conjecture and a recurrence relation connected to the Painlevé VI differential equation we obtain the asymptotic behaviour, accurate to order ${\cal O}(\ell^{-3})$, of the Rényi entropies $S_n(\ell)$ for large block lengths $\ell$. For n=1,2,3,10 this constitutes the 3,6,10,48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyze in some detail both for finite $n$ and in the limit $n\to\infty$.

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