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arXiv:2105.03016 · Physical review. B./Physical review. B

Low-temperature domain-wall freezing and nonequilibrium dynamics in the transverse-field Ising model material CoNb 2 O 6

Colin L. Sarkis, S. Säubert, V. Williams, Eun Sang Choi, T. R. Reeder, Harikrishnan S. Nair, K. A. Ross

Published Dec 16, 2021• 8 citations
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Abstract

${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ is a rare realization of the transverse-field Ising model, making it a useful tool for studying both equilibrium and nonequilibrium many-body quantum physics. Despite a large body of work dedicated to characterizing this material, details of the ordered states in the presence of relatively weak transverse fields have not been discussed in detail. Here, we present a detailed study of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ via ac susceptibility measurements in order to further characterize its low-temperature behavior in the presence of a transverse field. Specifically, we call attention to an unconventional freezing transition in zero field below ${T}_{F}=1.2$ K, occurring within the well-known commensurate antiferromagnetic (CAFM) state that onsets at ${T}_{N2}=1.9$ K. We performed a series of transverse-field quenches into this frozen state, which resulted in a slowly relaxing susceptibility, ${\ensuremath{\chi}}^{\ensuremath{'}}(t)$, that followed a logarithmic decay within the time range measured. We discuss the frozen state in the context of the freezing of previously discussed ``free'' chains arising from domain walls between the four degenerate sublattices of the CAFM state. We also attempted to observe Kibble-Zurek scaling by quenching the transverse field into the frozen state at different rates. This produced a null result; the behavior can be fully explained by coarsening of domains over the time scale of the quenches. The absence of a clear Kibble-Zurek scaling is itself surprising, given the proposed ubiquity of the phenomenon for general second-order phase transitions.

DOI
10.1103/physrevb.104.214424

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We analyze the quantum phase transitions taking place in a one-dimensional transverse-field Ising model with long-range couplings that decay algebraically with distance. We are interested in the Kibble-Zurek universal scaling laws emerging in nonequilibrium dynamics and in the potential for the unambiguous observation of such behavior in a realistic experimental setup based on trapped ions. To this end, we determine the phase diagram of the model and the critical exponents characterizing its quantum phase transitions by means of density-matrix renormalization group calculations and finite-size scaling theory, which allows us to obtain good estimates for different range of ferromagnetic and antiferromagnetic interactions. Beyond critical equilibrium properties, we tackle a nonequilibrium scenario in which quantum Kibble-Zurek scaling laws may be retrieved. Here, it is found that the predicted nonequilibrium universal behavior, i.e., the scaling laws as a function of the quench rate and critical exponents, can be observed in systems comprising an experimentally feasible number of spins. Finally, a scheme is introduced to simulate the algebraically decaying couplings accurately by means of a digital quantum simulation with trapped ions. Our results suggest that quantum Kibble-Zurek physics can be explored and observed in state-of-the-art experiments with trapped ions realizing long-range Ising models.
We consider the finite-time quench dynamics in the quantum transverse field Ising model which exhibits a second order phase transition from a paramagnetic to a ferromagnetic phase, as the transverse magnetic field is decreased. These dynamics have been thoroughly investigated in previous studies when the critical point is crossed during the quench; here, we quench the system from deep in the paramagnetic phase to just above the critical field so that the system remains in the gapped phase throughout the quench duration. On linearly quenching the infinitely large system, we find that the behavior of mean longitudinal defect density and mean transverse magnetization at the end of the quench falls into three distinct scaling regimes as the quench time is increased. For sufficiently small quench times, these observables remain roughly constant, but for larger quench times, a crossover occurs from the Kibble-Zurek scaling law to the quadratic quench rate law when the Kibble-Zurek time is of the order of relaxation time at the final quench field. These results are shown analytically using power series and uniform asymptotic expansions of the exact solution of the model, and also compared with an adiabatic perturbation theory in the third regime. We find that the above mentioned scaling regimes hold for quenches within the ferromagnetic phase also, and provide a general scaling argument for crossover from the Kibble-Zurek regime to an adiabatic regime for slow quenches within a gapped phase.
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