arXiv subjects

Jonathan Wurtz

Publications and source records attributed to Jonathan Wurtz.

22 records · Page 2Linked to original sources

arXiv2020

Emergent conservation laws and nonthermal states in the mixed-field Ising model

This paper presents a method of computing approximate conservation laws and eigenstates of integrability-broken models using the concept of adiabatic continuation. Given some Hamiltonian, eigenstates and conserved operators may be computed by using those of a simple Hamiltonian close by in parameter space, dressed by some unitary rotation. However, most adiabatic continuation analyses only use this unitary implicitly. In this work, approximate adiabatic gauge potentials are used to construct a state dressing using variational methods, to compute eigenstates via a rotated truncated spectrum approximation. These methods allow construction of both low and high-energy approximate nonthermal eigenstates, as well as quasi-local almost-conserved operators, in models where integrability may be non-perturbatively broken. These concepts will be demonstrated in the mixed-field Ising model.

cond-mat.str-el↗

arXiv2019

Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics

Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a unitary rotation, which leads to effective dynamics in a computationally tractable reduced Hilbert space. The generator of these rotations are computed variationally and thus go beyond standard perturbative methods; the error is controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with on-site disorder, we find indications of a lack of observable many-body localization in the thermodynamic limit due to the inevitable mixture of different spinon sectors. Second, in the low-energy sector of the XY spin model with a broken U(1)-symmetry, we analyze ground state response functions by combining the variational SW transformation with the truncated spectrum approach.

cond-mat.str-el↗

arXiv2018

Quantum Hydrodynamics in Spin Chains with Phase Space Methods

Connecting short time microscopic dynamics with long time hydrodynamics in strongly correlated quantum systems is one of the outstanding questions. In particular, it is very difficult to determine various hydrodynamic coefficients like the diffusion constant or viscosity starting from a microscopic model: exact quantum simulations are limited to either small system sizes or to short times, which are insufficient to reach asymptotic behavior. In this Letter, we show that these difficulties, at least for a particular model, can be circumvented by using the cluster truncated Wigner approximation (CTWA), which maps quantum Hamiltonian dynamics into classical Hamiltonian dynamics in auxiliary high-dimensional phase space. We apply CTWA to a XXZ next-nearest-neighbor spin 1/2 chain and find behavior consisting of short time spin relaxation which gradually crosses over to emergent diffusive behavior at long times. For a random initial state we show that CTWA correctly reproduces the whole spin spectral function. Necessary in this construction is sampling from properly fluctuating initial conditions: the Dirac mean-field (variational) ansatz, which neglects such fluctuations, leads to incorrect predictions.

cond-mat.stat-mech↗

arXiv2018

Cluster Truncated Wigner Approximation in Strongly Interacting Systems

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with the increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.

quant-ph↗