Keldysh field theory of a driven dissipative Mott insulator: Nonequilibrium response and phase transitions

Abstract

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 last 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 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 τ d that increases with 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.

$${\mathcal{P}}{\mathcal{T}}$$-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain

“…c 1 h the system described by the Hamiltonian (10) experiences a phase transition from a Mott insulator to a bad metal state. This is in stark contrast with the behavior of the half-filled Hermitian fermionic Hubbard chain that does not exhibit a phase transition under the applied drive 28 but in agreement with Keldysh field-theory based analyses of driven dissipative Mott insulator systems 29 . Approaching the transition, the Mott gap Δ collapses, showing the critical…”

“…The expected initial response is the Bloch-like oscillations, which have to cross over into the eventual steady-state dc current, the response that is absent in the non-dissipative counterpart 28,30 . For driven dissipative Mott systems, nonequilibrium field theoretical approaches have been developed, primarily based on the Keldysh dynamical mean-field theory [31][32][33] for the Hubbard model, or more recently, the Keldysh generalization of the Ambegaokar-Eckern-Schön (AES) rotor model for normal granular metals 29 indeed demonstrating the envisioned behavior. It would be very interesting to investigate whether the nonequilibrium insulator-to-metal transitions in these Keldysh-based models are the true phase transitions or crossovers, and in the former case, how do the critical exponents of the field driven nonequilibrium Mott transition in the Keldysh approach compare with those obtained from the PT -symmetric Hubbard model 2 .…”

Superconductor-like effects in an AC driven normal Mott-insulating quantum dot array

“…The nonequilibrium response of strongly correlated quantum systems is a challenging problem requiring understanding of the many-body excitation spectra, wavefunctions, dynamical bottlenecks and dissipative processes. Driven Mott insulators are a prototypical example, exhibiting diverse phenomena that are otherwise not present in their equilibrium or linear-response regimes such as field and current driven insulator-metal transitions [1][2][3][4][5], Bloch oscillations or Wannier-Stark quantization [6][7][8][9][10][11] and current enhanced diamagnetism [12]. A number of recent studies of optically excited Mott insulating half-filled Hubbard models have proposed a new route to superconductivity through doublon creation [13][14][15][16][17][18][19][20][21][22], possibly an exotic η-pairing state originally proposed by Yang [23] for the one-dimensional case.…”

“…Theoretical understanding of driven Mott insulators has received a significant impetus by developments in the numerical Keldysh dynamical mean field theory (KDMFT) approach [8,9,11,[29][30][31][32] and tensor network techniques [25], and analytic Bethe-ansatz techniques [33] including the effective PT -symmetric descriptions [34,35]. Recently an alternate analytical large-N effective Keldysh field theory approach [6] has been developed based on the well-known Ambegaokar-Eckern-Schön (AES) rotor model [36,37] for electron transport in mesoscopic quantum dot arrays, effectively a dissipative Mott insulator system. This Keldysh formalism has been demonstrated to capture numerous nonequilibrium DC phenomena including Bloch-like oscillations and the field-driven insulator to metal transition, reported in earlier KDMFT studies.…”

“…Our starting point is the Keldysh-AES model [6,38] for a one-dimensional array of normal mesoscopic quantum dots each with a charging energy E C and interdot dimensionless conductance g,…”