# Publications by Berislav Buca

## Heating-Induced Long-Range η Pairing in the Hubbard Model.

Physical review letters **123** (2019) 030603-

We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady states with long-range correlations between η pairs. We induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal η correlations. These correlations were first recognized in the superconducting eigenstates described in Yang's seminal Letter [Phys. Rev. Lett. 63, 2144 (1989)PRLTAO0031-900710.1103/PhysRevLett.63.2144], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.

## Non-stationary coherent quantum many-body dynamics through dissipation.

Nature communications **10** (2019) 1730-

The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.

## Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton.

Physical review. E **100** (2019) 020103-

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit "Doob-transformed" dynamics that optimally realizes rare dynamical events.

## Dissipation Induced Nonstationarity in a Quantum Gas

PHYSICAL REVIEW LETTERS **123** (2019) ARTN 260401

## Symmetries and conservation laws in quantum trajectories: Dissipative freezing

Physical Review A American Physical Society **100** (2019) 042113

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.

## Quantum probe spectroscopy for cold atomic systems

NEW JOURNAL OF PHYSICS **20** (2018) ARTN 103006

## Strongly correlated non-equilibrium steady states with currents - quantum and classical picture

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS **227** (2018) 421-444

## Exact matrix product decay modes of a boundary driven cellular automaton

Journal of Physics A: Mathematical and Theoretical **50** (2017)

© 2017 IOP Publishing Ltd. We study integrability properties of a reversible deterministic cellular automaton (Rule 54 of (Bobenko et al 1993 Commun. Math. Phys. 158 127)) and present a bulk algebraic relation and its inhomogeneous extension which allow for an explicit construction of Liouvillian decay modes for two distinct families of stochastic boundary driving. The spectrum of the many-body stochastic matrix defining the time propagation is found to separate into sets, which we call orbitals, and the eigenvalues in each orbital are found to obey a distinct set of Bethe-like equations. We construct the decay modes in the first orbital (containing the leading decay mode) in terms of an exact inhomogeneous matrix product ansatz, study the thermodynamic properties of the spectrum and the scaling of its gap, and provide a conjecture for the Bethe-like equations for all the orbitals and their degeneracy.

## Charge and spin current statistics of the open Hubbard model with weak coupling to the environment.

Physical review. E **95** (2017) 052141-052141

Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.

## Connected correlations, fluctuations and current of magnetization in the steady state of boundary driven XXZ spin chains

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016) ARTN 023102

## Spectral analysis of finite-time correlation matrices near equilibrium phase transitions

EPL **108** (2014) ARTN 20006

## Exactly solvable counting statistics in open weakly coupled interacting spin systems.

Physical review letters **112** (2014) 067201-

We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg (XXZ) spin-1/2 chain, we explicitly derive the third-order nonlinear corrections to the current statistics.

## A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains

NEW JOURNAL OF PHYSICS **14** (2012) ARTN 073007

## Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries

ArXiv (0)

We study the null space degeneracy of open quantum systems with multiple non-Abelian, strong symmetries. By decomposing the Hilbert space representation of these symmetries into an irreducible representation involving the direct sum of multiple, commuting, invariant subspaces we derive a tight lower bound for the stationary state degeneracy. We apply these results within the context of open quantum many-body systems, presenting three illustrative examples: a fully-connected quantum network, the XXX Heisenberg model and the Hubbard model. We find that the derived bound, which scales at least cubically in the system size the $SU(2)$ symmetric cases, is often saturated. Moreover, our work provides a theory for the systematic block-decomposition of a Liouvillian with non-Abelian symmetries, reducing the computational difficulty involved in diagonalising these objects and exposing a natural, physical structure to the steady states - which we observe in our examples.

## The isolated Heisenberg magnet as a quantum time crystal

ArXiv (0)

We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain. We discuss how the ensuing persistent oscillations that violate one of the most fundamental laws of physics could be observed experimentally and identify potential metrological applications.

## Integrable non-equilibrium steady state density operators for boundary driven XXZ spin chains: observables and full counting statistics

ArXiv (0)

We will review some known exact solutions for the steady state of the open quantum Heisenberg $XXZ$ spin chain coupled to a pair of baths [Phys. Rev. Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master equation. We also review how to calculate some relevant physical observables and provide the statistics of spin current assuming the spin chain is weakly coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].

## Non-stationary dynamics and dissipative freezing in squeezed superradiance

ArXiv (0)

In this work, we study the driven-dissipative dynamics of a coherently-driven spin ensemble with a squeezed, superradiant decay. This decay consists of a sum of both raising and lowering collective spin operators with a tunable weight. The model presents different critical non-equilibrium phases with a gapless Liouvillian that are associated to particular symmetries and that give rise to distinct kinds of non-ergodic dynamics. In Ref. [1] we focus on the case of a strong-symmetry and use this model to introduce and discuss the effect of dissipative freezing, where, regardless of the system size, stochastic quantum trajectories initialized in a superposition of different symmetry sectors always select a single one of them and remain there for the rest of the evolution. Here, we deepen this analysis and study in more detail the other type of non-ergodic physics present in the model, namely, the emergence of non-stationary dynamics in the thermodynamic limit. We complete our description of squeezed superradiance by analysing its metrological properties in terms of spin squeezing and by analysing the features that each of these critical phases imprint on the light emitted by the system.

## Quantum Synchronisation Enabled by Dynamical Symmetries and Dissipation

ArXiv (0)

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying symmetry-based conditions which, when satisfied, guarantee completely synchronous, entangled limit cycles between the individual constituents of a generic open quantum system - no restrictions are placed on its microscopic details. We describe these systems as posssessing a strong dynamical symmetry and we prove that, to first order, they are completely robust to symmetry-breaking perturbations. Using these ideas we identify two central examples where synchronisation arises via this qualitatively new mechanism: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases, due to their dynamical symmetries, perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their non-linear responses elicit long-lived signatures of both phase and frequency-locking.