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Register a new userErgodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
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Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unitarity, leading to the appearance of prethermalization plateaux for local observables.
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An important challenge in the field of many-body quantum dynamics is to identify non-ergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group methods predict a partially localized, non-ergodic regime known as a quantum critical glass (a critical variant of MBL). This regime features a tree-like hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative non-ergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times. We identify the relevant length and time scales for thermalization: even if such chains eventually thermalize, they can exhibit non-ergodic dynamics up to parametrically long time scales with a non-analytic dependence on disorder strength.
Whether one is interested in quantum state preparation or in the design of efficient heat engines, adiabatic (reversible) transformations play a pivotal role in minimizing computational complexity and energy losses. Understanding the structure of these transformations and identifying the systems for which such transformations can be performed efficiently and quickly is therefore of primary importance. In this paper we focus on finding optimal paths in the space of couplings controlling the systems Hamiltonian. More specifically, starting from a local Hamiltonian we analyze directions in the space of couplings along which adiabatic transformations can be accurately generated by local operators, which are both realizable in experiments and easy to simulate numerically. We consider a non-integrable 1D Ising model parametrized by two independent couplings, corresponding to longitudinal and transverse magnetic fields. We find regions in the space of couplings characterized by a very strong anisotropy of the variational adiabatic gauge potential (AGP), generating the adiabatic transformations, which allows us to define optimal adiabatic paths. We find that these paths generally terminate at singular points characterized by extensive degeneracies in the energy spectrum, splitting the parameter space into adiabatically disconnected regions. The anisotropy follows from singularities in the AGP, and we identify special robust weakly-thermalizing and non-absorbing many-body dark states which are annihilated by the singular part of the AGP and show that their existence extends deep into the ergodic regime.
We prove a local version of Gowers Ramsey-type theorem [21], as well as loc
The dynamics of an open system crucially depends on the correlation function of its environment, $C_B(t)$. We show that for thermal non-Harmonic environments $C_B(t)$ may not decay to zero but to an offset, $C_0>0$. The presence of such offset is determined by the environment eigenstate structure, and whether it fulfills or not the eigenstate thermalization hypothesis. Moreover, we show that a $C_0>0$ could render the weak coupling approximation inaccurate and prevent the open system to thermalize. Finally, for a realistic environment of dye molecules, we show the emergence of the offset by using matrix product states (MPS), and discuss its link to a 1/f noise spectrum that, in contrast to previous models, extends to zero frequencies. Thus, our results may be relevant in describing dissipation in quantum technological devices like superconducting qubits, which are known to be affected by such noise.
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. Random channels appear in a wide variety of applications, from quantum chaos to holographic dualities in theories of quantum gravity to operator dynamics, to random local circuits for their potential to demonstrate quantum supremacy. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a rank-one (entanglement breaking) channel. Using this, we derive the limiting behavior of translation invariant channels, and stochastically independent random channels. We then use our formalism to describe the thermodynamic limit of ergodic Matrix Product States. We derive formulas for the expectation value of a local observable and prove that the 2-point correlations of local observables decay exponentially. We then analytically compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy (i.e., R{e}nyi or von Neumann) across an arbitrary cut can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are meta-stable, and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned. To obtain these results we bridge quantum information theory to dynamical systems and random matrix theory.
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