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Bulletin of the American Physical Society

Finite-temperature spin dynamics near the quantum critical point of transverse field Ising chain with a small longitudinal field

Márton Kormos, Jianda Wu, Qimiao Si A

Published Mar 4, 2014• 0 citations
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A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.
We show for the models here investigated that the teleportation-based quantum critical point (QCP) detectors can properly estimate the locations of the QCPs when we are not even close to the thermodynamic limit (infinite spin chains) and when we only have access to finite temperature data. Specifically, by working with spin chains with about ten qubits and in equilibrium with a thermal reservoir at temperature T, we show that it is possible to locate with an error of only a few percents the correct spots of the QCPs for almost all the models studied here. The spin chains we investigate are given by the XXZ model with or without an external longitudinal magnetic field as well as the XX model, the XY model and the Ising model, all of them subjected to an external transverse magnetic field.
We study the short-time Loschmidt dynamics after a small sudden quench near a quantum critical point. We show that the initial quadratic growth of the Loschmidt rate function is governed by the variance of the quench operator per system size. For a local quench operator, this variance density is exactly equal to the spatial sum of the equal-time connected two-point correlation function in the initial ground state. This relation connects the early-time Loschmidt response to static critical correlations. Assuming power-law correlations at criticality, we classify the finite-size scaling of the short-time coefficient by the scaling dimension of the quench operator. In one dimension, the coefficient is finite, logarithmically enhanced, or algebraically enhanced with system size. We illustrate this operator dependence in the transverse-field Ising chain, where transverse-field and longitudinal-field quenches couple to different critical operators. We also discuss the first correction beyond the quadratic regime using the fourth cumulant of the post-quench Hamiltonian.