arXiv subjects

F. H. L. Essler

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

At least 19 recordsLinked to original sources

arXiv2026

Quench Spectroscopy of Magnetic Excitations on a Superconducting Quantum Processor

The elementary excitation spectrum of a many-body quantum system encodes many key properties, including phenomena as diverse as transport, thermalisation and ground state structure. Excitation spectra of strongly correlated systems are typically encoded in dynamical structure factors, which are demanding to measure experimentally and challenging to compute classically. Here we use quench spectroscopy on a superconducting quantum processor to extract excitation spectra of spin chains of $L=101$ spins. By tailoring the combination of quench protocol and observable, we selectively access distinct excitation sectors across several phases of the spin-$1/2$ XXZ chain, resolving free magnons, multi-magnon bound states, and two-spinon continua. Notably, we demonstrate that the protocol does not rely on ground state preparation: in the classically challenging gapless regime, we extract spectra directly from the quench dynamics of easily prepared product states, a procedure that is natural and straightforward on quantum hardware. Our work establishes quench spectroscopy as a fast and flexible probe of many-body excitation spectra on digital quantum hardware, introduces a novel quench protocol that does not require costly state preparation routines, and provides a scalable route towards regimes where classical simulation may become intractable.

quant-ph↗

arXiv2025

Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations diverge linearly in particular time differences. This behaviour can be understood by means of a simple semiclassical analysis based on the kinematics and scattering of wave packets of quasiparticles. We verify that our wave packet analysis correctly predicts the long-time limit of the four-point function in the transverse field Ising model through a form factor expansion. We present evidence in favour of the same behaviour in integrable quantum field theories. In addition, we extend our discussion to experimental protocols where two times of the four-point function coincide, e.g. 2D coherent spectroscopy and pump-probe experiments. Finally, focusing on the Ising model, we discuss subleading corrections that grow as the square root of time differences. We show that the subleading corrections can be correctly accounted for by the same semiclassical analysis, but also taking into account wave packet spreading.

cond-mat.str-el↗

arXiv2023

Statistics of matrix elements of local operators in integrable models

We study the statistics of matrix elements of local operators in the basis of energy eigenstates in a paradigmatic integrable many-particle quantum theory, the Lieb-Liniger model of bosons with repulsive delta-function interaction. Using methods of quantum integrability we determine the scaling of matrix elements with system size. As a consequence of the extensive number of conservation laws the structure of matrix elements is fundamentally different from, and much more intricate than, the predictions of the eigenstate thermalization hypothesis for generic models. We uncover an interesting connection between this structure for local operators in interacting integrable models, and the one for local operators that are not local with respect to the elementary excitations in free theories. We find that typical off-diagonal matrix elements $\langle\boldsymbolμ|O|\boldsymbolλ\rangle$ in the same macro-state scale as $\exp(-c^{ O}L\ln(L)-LM^{O}_{\boldsymbolμ,\boldsymbolλ})$ where the probability distribution function for $M^{O}_{\boldsymbolμ,\boldsymbolλ}$ are well described by Fréchet distributions and $c^{O}$ depends only on macro-state information. In contrast, typical off-diagonal matrix elements between two different macro-states scale as $\exp(-d^{ O}L^2)$, where $d^{O}$ depends only on macro-state information. Diagonal matrix elements depend only on macro-state information up to finite-size corrections.

cond-mat.stat-mech↗

arXiv2017

Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet

Confinement is a process by which particles with fractional quantum numbers bind together to form quasiparticles with integer quantum numbers. The constituent particles are confined by an attractive interaction whose strength increases with increasing particle separation and as a consequence, individual particles are not found in isolation. This phenomenon is well known in particle physics where quarks are confined in baryons and mesons. An analogous phenomenon occurs in certain magnetic insulators; weakly coupled chains of spins S=1/2. The collective excitations in these systems is spinons (S=1/2). At low temperatures weak coupling between chains can induce an attractive interaction between pairs of spinons that increases with their separation and thus leads to confinement. In this paper, we employ inelastic neutron scattering to investigate the spinon confinement in the quasi-1D S=1/2 XXZ antiferromagnet SrCo2V2O8. Spinon excitations are observed above TN in quantitative agreement with established theory. Below TN the pairs of spinons are confined and two sequences of meson-like bound states with longitudinal and transverse polarizations are observed. Several theoretical approaches are used to explain the data. A new theoretical technique based on Tangent-space Matrix Product States gives a very complete description of the data and provides good agreement not only with the energies of the bound modes but also with their intensities. We also successfully explained the effect of temperature on the excitations including the experimentally observed thermally induced resonance between longitudinal modes below TN ,and the transitions between thermally excited spinon states above TN. In summary, our work establishes SrCo2V2O8 as a beautiful paradigm for spinon confinement in a quasi-1D quantum magnet and provides a comprehensive picture of this process.

cond-mat.str-el↗

arXiv2016

On Truncated Generalized Gibbs Ensembles in the Ising Field Theory

We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green's function $G(x) = \langle ψ^{\dagger}(x) ψ(0) \rangle$ of the complex fermion field $ψ(x)$. We find that both truncated GGEs are able to recover $G(x)$, but for a given number of charges the semi-local version performs better.

cond-mat.stat-mech↗

arXiv2015

Generalized Gibbs Ensembles for Quantum Field Theories

We consider the non-equilibrium dynamics in isolated systems, described by quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In a presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra-)local in the usual sense of QFT, but fulfil a significantly weaker form of locality. We discuss implications of our results for integrable QFTs in one spatial dimension.

cond-mat.quant-gas↗

arXiv2015

Spin-charge separated quasiparticles in one dimensional quantum fluids

We revisit the problem of dynamical response in spin-charge separated one dimensional quantum fluids. In the framework of Luttinger liquid theory, the dynamical response is formulated in terms of noninteracting bosonic collective excitations carrying either charge or spin. We argue that, as a result of spectral nonlinearity, long-lived excitations are best understood in terms of generally strongly interacting fermionic holons and spinons. This has far reaching ramifications for the construction of mobile impurity models used to determine threshold singularities in response functions. We formulate and solve the appropriate mobile impurity model describing the spinon threshold in the single-particle Green's function. Our formulation further raises the question whether it is possible to realize a model of noninteracting fermionic holons and spinons in microscopic lattice models of interacting spinful fermions. We investigate this issue in some detail by means of density matrix renormalization group (DMRG) computations.

cond-mat.str-el↗

arXiv2014

Quench Dynamics in a Model with Tuneable Integrability Breaking

We consider quantum quenches in an integrable quantum chain with tuneable-integrability-breaking interactions. In the case where these interactions are weak, we demonstrate that at intermediate times after the quench local observables relax to a prethermalized regime, which can be described by a density matrix that can be viewed as a deformation of a generalized Gibbs ensemble. We present explicit expressions for the approximately conserved charges characterizing this ensemble. We do not find evidence for a crossover from the prethermalized to a thermalized regime on the time scales accessible to us. Increasing the integrability-breaking interactions leads to a behaviour that is compatible with eventual thermalization.

cond-mat.stat-mech↗

arXiv2012

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

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.

cond-mat.quant-gas↗

arXiv2012

Discrete Symmetry Breaking Transitions Between Paired Superfluids

We explore the zero-temperature phase diagram of bosons interacting via Feshbach resonant pairing interactions in one dimension. Using DMRG (Density Matrix Renormalization Group) and field theory techniques we characterize the phases and quantum phase transitions in this low-dimensional setting. We provide a broad range of evidence in support of an Ising quantum phase transition separating distinct paired superfluids, including results for the energy gaps, correlation functions and entanglement entropy. In particular, we show that the Ising correlation length, order parameter and critical properties are directly accessible from a ratio of the atomic and molecular two-point functions. We further demonstrate that both the zero-momentum occupation numbers and the visibility are in accordance with the absence of a purely atomic superfluid phase. We comment on the connection to recent studies of boson pairing in a generalized classical XY model.

cond-mat.quant-gas↗

arXiv2012

Finite wave vector pairing in doped two-leg ladders

We consider the effects of Umklapp processes in doped two-leg fermionic ladders. These may emerge either at special band fillings or as a result of the presence of external periodic potentials. We show that such Umklapp processes can lead to profound changes of physical properties and in particular stabilize pair-density wave phases.

cond-mat.str-el↗

arXiv2011

Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians

We explore the Mott insulating state of single-band bosonic pairing Hamiltonians using analytical approaches and large scale density matrix renormalization group calculations. We focus on the second Mott lobe which exhibits a magnetic quantum phase transition in the Ising universality class. We use this feature to discuss the behavior of a range of physical observables within the framework of the 1D quantum Ising model and the strongly anisotropic Heisenberg model. This includes the properties of local expectation values and correlation functions both at and away from criticality. Depending on the microscopic interactions it is possible to achieve either antiferromagnetic or ferromagnetic exchange interactions and we highlight the possibility of observing the E8 mass spectrum for the critical Ising model in a longitudinal magnetic field.

cond-mat.str-el↗

arXiv2011

Ising Deconfinement Transition Between Feshbach-Resonant Superfluids

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group (DMRG) and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.

cond-mat.quant-gas↗

arXiv2010

Low-Temperature Dynamical Structure Factor of the Two-Leg Spin-1/2 Heisenberg Ladder

We determine the dynamical structure factor of the two-leg spin-1/2 Heisenberg ladder at low temperatures in the regime of strong rung coupling. The dominant feature at zero temperature is the coherent triplon mode. We show that the lineshape of this mode broadens in a non-symmetric way at finite temperatures and that the degree of asymmetry increases with temperature. We also show that at low frequencies a temperature induced resonance akin to the Villain mode in the spin-1/2 Heisenberg Ising chain emerges.

cond-mat.str-el↗

arXiv2010

Effects of thermal phase fluctuations in a 2D superconductor: an exact result for the spectral function

We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi energy we obtain an exact expression for the spectral function integrated over the momentum component perpendicular to the Fermi surface.

cond-mat.supr-con↗

arXiv2010

Threshold Singularities in the One Dimensional Hubbard Model

We consider excitations with the quantum numbers of a hole in the one dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model (electron gas with delta-function interactions).

cond-mat.str-el↗

arXiv2009

Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories

We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.

cond-mat.str-el↗

arXiv2009

On thermal fluctuations in quantum magnets

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.

cond-mat.str-el↗