Integrable nonunitary open quantum circuits

Abstract

We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved superoperator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the local dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions to the local coherent dynamics or by removing the dephasing. In particular, even circuits built from convex combinations of local free-fermion unitaries are nonintegrable. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.

Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

“…There are also additional technical problems: correlations of complex eigenvalues are weakened, and the necessary unfolding of eigenvalues may be problematic [46] in particular when the eigenvalue distribution is not radially symmetric. However, these problems have been ameliorated in the last years with the introduction of spectral observables that do not require unfolding for short-range correlators, such as the ratio of spacings between nearest-neighbor eigenvalues [69], which have found applications in the study of collective-spin Liouvillians [70], non-Hermitian Anderson transitions [71][72][73], directed random graphs [74], nonunitary open quantum circuits [75,76], two-color QCD [38], and the classicalquantum transition [51]. The study of long-range correlators such as the number variance [77][78][79][80] or spectral form factor [81,82] (which requires unfolding) further suggests that some weakened form of spectral rigidity is still present in non-Hermitian systems and will be subject of a separate publication [83].…”

Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos

“…Non-Hermitian physics has advanced significantly in recent years in the study of optics [15][16][17], acoustics [18,19], parity-time-symmetric systems [20,21], mesoscopic physics [22][23][24][25], cold atoms [26,27], driven dissipative systems [28][29][30][31][32], biological systems [33], disordered systems [5]. Recent studies on spectral properties have focused on the shape of eigenvalue density, the spectral gap, and the spacing between nearest-neighbour eigenvalues [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The goal of this letter is to introduce and analyze a simple indicator that characterizes the level statistics of non-Hermitian matrices up to an arbitrary energy (and, equivalently, time) scale, and show that it captures universal signatures of dissipative quantum chaos.…”

Integrable spin chains and cellular automata with medium range interaction

“…This idea goes back to the light cone regularization of integrable QFT's [65][66][67]. More recently the same idea was also applied to dissipative systems [68].…”