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Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices | Raphaël Menu
; Tommaso Roscilde
; | Date: |
3 Jan 2023 | Abstract: | The study of non-equilibrium dynamics is one of the most important challenges
of modern quantum many-body physics, in relationship with fundamental questions
in quantum statistical mechanics, as well as with the fields of quantum
simulation and computing. In this work we propose a Gaussian Ansatz for the
study of the nonequilibrium dynamics of quantum spin systems. Within our
approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such
that a coherent spin state -- chosen as the initial state of the dynamics --
represents the bosonic vacuum. The state of the system is then postulated to
remain a bosonic Gaussian state at all times, an assumption which is exact when
the bosonic Hamiltonian is quadratic; and which is justified in the case of a
nonlinear Hamiltonian if the boson density remains moderate. We test the
accuracy of such an Ansatz in the paradigmatic case of the $S=1/2$
transverse-field Ising model, in one and two dimensions, initialized in a state
aligned with the applied field. We show that the Gaussian Ansatz, when applied
to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is
able to reproduce faithfully the evolution of the state, including its
relaxation to the equilibrium regime, for fields larger than the critical field
for the paramagnetic-ferromagnetic transition in the ground state. In
particular the spatio-temporal pattern of correlations reconstructed via the
Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations,
exhibiting the softening of the excitation gap upon approaching the critical
field. Our results suggest that the Gaussian Ansatz correctly captures the
essential effects of nonlinearities in quantum spin dynamics; and that it can
be applied to the study of fundamental phenomena such as quantum thermalization
and its breakdown. | Source: | arXiv, 2301.01363 | Services: | Forum | Review | PDF | Favorites |
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