Topological transitions in weakly monitored free fermions

Abstract

We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. In the presence of unitary dynamics, the two topologically distinct phases are separated by a region with sub-volume scaling of the entanglement entropy. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy. We further show that the phase diagram is qualitatively captured by an analytically tractable non-Hermitian model obtained via post-selecting the measurement outcome. Finally we introduce a partial-post-selection continuous mapping, that uniquely associates topological indices of the non-Hermitian Hamiltonian to the distinct phases of the stochastic measurement-induced dynamics.

Entanglement dynamics with string measurement operators

“…Recently, an increasing number of works have been focusing on MIPTs in fermionic systems described by quadratic Hamiltonians on a lattice, undergoing quantum trajectories under the action of random measurements of onsite quadratic operators [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. One of the reasons of this interest relies in the Gaussian structure of the states of such systems that, being entirely determined by two-point correlation functions, are suitable for a semi-analytical treatment up to large lattice sizes (of the order of hundreds of sites) [62][63][64][65][66][67][68].…”

Entanglement Phase Transitions in Non-Hermitian Kitaev Chains

“…Moreover, in non-Hermitian systems with spatially uniform or quasiperiodic randomness [ 55 , 56 , 57 , 58 ], entanglement phase transitions beyond the conventional volume-law to area-law scheme could emerge due to the interplay between disorder and non-Hermitian effects. In addition, alternated and re-entrant entanglement transitions may be engineered and controlled by time-periodic driving fields in non-Hermitian Floquet systems [ 59 ].…”

“…Open quantum systems described by non-Hermitian Hamiltonians constitute an important context for exploring entanglement phase transitions. Various types of non-Hermiticity-induced entanglement transitions have been identified in gapped or critical non-Hermitian systems made up of lattice fermions and quantum spin chains [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64]. In a non-Hermitian system with spatial nonreciprocity, the emergence of non-Hermitian skin effects was found to accompany the transition from a volume-law entangled to an area-law entangled phase in one spatial dimension [52].…”

The impact of different unravelings in a monitored system of free fermions

“…In this framework, an extensive number of works has been focusing on local measurements (either discrete or continuous in time) performed in monitored quantum circuits [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], as well as in non-interacting [17,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] and interacting [49][50][51][52][53][54][55] Hamiltonian systems. Moreover, there exists a deep connection between measurementinduced phases and the encoding/decoding properties of a quantum channel [56][57][58]…”

“…Among the various theoretical models of monitored quantum systems, considerable coverage has been dedicated to the dynamics of fermionic Gaussian states, in the presence of quadratic Hamiltonians and Gaussianpreserving measurement processes (see, e.g., Refs. [31,34,36,[39][40][41][42][43][44][45][46][47][48][69][70][71][72]), as they are amenable to an accurate numerical treatment up to relatively large sizes. In this framework, for short-range Hamiltonians and local measurements, area-law (saturation to a finite value) or logarithmic scaling of the asymptotic entanglement entropy with the system size have been reported.…”