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arXiv:1510.08355 · Physical review. B./Physical review. B

Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems

Vikram Tripathi, Alexey Galda, Himadri Barman, V. M. Vinokur

Published Jul 5, 2016• 27 citations
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Abstract

We describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity $(\mathcal{P})$ and time-reversal $(\mathcal{T})$ operations. The dynamic Mott transition is identified as a $\mathcal{PT}$ symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken $\mathcal{PT}$ symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdown and describe the resulting critical behavior of transport characteristics. The obtained critical exponent is in an excellent agreement with experimental findings.

DOI
10.1103/physrevb.94.041104

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We describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P)(\mathcal{P})(P) and time-reversal (T)(\mathcal{T})(T) operations. The dynamic Mott transition is identified as a PT\mathcal{PT}PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT\mathcal{PT}PT symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdown and describe the resulting critical behavior of transport characteristics. The obtained critical exponent is in an excellent agreement with experimental findings.
PT{\mathcal{P}}{\mathcal{T}}PT-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain
Abstract Nonequilibrium phase transitions in open dissipative systems can be described as instabilities in the spectra and wavefunctions of effective non-Hermitian Hamiltonians invariant under simultaneous parity ( P\boldsymbol{\mathcal{P}}P P ) and time-reversal ( T\boldsymbol{\mathcal{T}}T T ) transformations. The degree of non-Hermiticity reflects the strength of the external drive and dissipation, and the transition is described as a loss of the PT\boldsymbol{\mathcal{P}}\boldsymbol{\mathcal{T}}PT PT symmetry of the solutions corresponding to stationary low-drive dynamics. This approach has been successfully applied to spin, superconducting, and Mott insulator systems. However, the microscopic foundations for the employed phenomenological models are currently lacking. Here we propose a microscopic mechanism leading to the PT\boldsymbol{\mathcal{P}}\boldsymbol{\mathcal{T}}PT PT -symmetric effective model in the context of the nonequilibrium Mott transition in a dissipative Hubbard chain. Our model comprises a half-filled fermionic Hubbard chain subject to a constant electric field. The dissipation is introduced via the electron-phonon coupling. We obtain the explicit expressions for the non-Hermitian parameter in terms of the electron-phonon coupling strength and driving field. Analyzing the implications of microscopic model, we find a re-entrant Mott insulator with the increasing electric field for phonon density of states that increases slower than the square of the energy (such as in one or two dimensions), or varies non-monotonously with energy.
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time (PT\mathcal{PT}PT) symmetry if we compensate the system additionally with an overall gain term. By solving exactly the two-site Lindblad equation with fixed dissipation, we find that the dynamics of the rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in the scheme of non-Hermitian effective Hamiltonians. This instability is also observed in multisite systems and closely related to the PT\mathcal{PT}PT-symmetry breaking accompanied by appearance of complex eigenvalues of the effective Hamiltonian. Moreover, we unveil that the dynamical instability of the antiferromagnetic Mott phase comes from the PT\mathcal{PT}PT-symmetry breaking in highly excited bands, although the low-energy effective model of the non-Hermitian Hubbard model in the strongly interacting regime is always Hermitian. We also provide a quantitative estimation of the time for the observation of dynamical PT\mathcal{PT}PT-symmetry breaking which could be probed in experiments.
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-N\mathcal{N}N Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\ensuremath{\tau}}_{d}$ that increases with N.\mathcal{N}.N. Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.
The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory for the DMT based on the parity reflection-time reversal (PT\mathcal{P}TPT) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class.
The effect of \mathcal{PT} 𝒫 𝒯 -symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of \mathcal{PT} 𝒫 𝒯 symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected \mathcal{PT} 𝒫 𝒯 -symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe \mathcal{PT} 𝒫 𝒯 -symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.
We study the nonequilibrium steady state of a Mott insulator coupled to a thermostat and driven by a constant electric field, starting from weak fields, until the dielectric breakdown, and beyond. We find that the conventional Zener picture does not describe the steady-state physics. In particular, the current at weak field is found to be controlled by the dissipation. Moreover, in connection with the electric-field-driven dimensional crossover, we find that the dielectric breakdown occurs when the field strength is on the order of the Mott gap of the corresponding lower-dimensional system. We also report a resonance and the meltdown of the quasiparticle peak when the field strength is half of this Mott gap.