We consider a class of quantum lattice models in 1+1 dimensions represented as local quantum circuits that enjoy a particular "dual-unitarity" property. In essence, this property ensures that both the evolution "in time" and that "in space" are given in terms of unitary transfer matrices. We show that for this class of circuits, generically non-integrable, one can compute explicitly all dynamical correlations of local observables. Our result is exact, non-pertubative, and holds for any dimension d of the local Hilbert space. In the minimal case of qubits (d=2) we also present a classification of all dual-unitary circuits which allows us to single out a number of distinct classes for the behaviour of the dynamical correlations. We find "non-interacting" classes, where all correlations are preserved, the ergodic and mixing one, where all correlations decay, and, interestingly, also classes that are are both interacting and non-ergodic.
COBISS.SI-ID: 3389028
We present an explicit time-dependent matrix product ansatz (tMPA) which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)]. Our construction is based on an explicit solution of real-space real-time inverse scattering problem. We consider two applications of this tMPA. Firstly, we provide the first exact and explicit computation of the dynamic structure factor in an interacting deterministic model, and secondly, we solve the extremal case of the inhomogeneous quench problem, where a semi-infinite lattice in the maximum entropy state is joined with an empty semi-infinite lattice. Both of these exact results rigorously demonstrate a coexistence of ballistic and diffusive transport behaviour in the model, as expected for normal fluids.
COBISS.SI-ID: 3367012
We introduce a novel class of exactly solvable many-body dynamical systems in discrete space-time. The model represents locally interacting matrix-valued degrees of freedom which take values on certain complex manifolds including, for example, the complex projective spaces and complex Grassmannian manifolds that arise as cosets of the unitary Lie group. We devise a general algebraic construction based on a discrete version of the zero-curvature condition, thereby manifestly ensuring integrability of the time-evolution. In the continuous-time limit, the matrix models reduce to the Hamiltonian field theory of the nonrelativistic sigma models on quotient manifolds which govern the generalized Landau-Lifshitz ferromagnets symmetric under the the global symmetry of unitary or symplectic Lie groups. The matrix models may accordingly be understood as their integrable Trotterization, i.e. they provide an explicit integration scheme in the form of a classical circuit composed of two-body symplectic maps. As our main application, we investigate transport properties of the Noether charges in unpolarized equilibrium ensembles. By carrying out a comprehensive numerical analysis, we find clear signature of an anomalous type of diffusion law that belongs to the Kardar-Parisi-Zhang universality class. Most surprisingly, this conclusion holds irrespectively of the symmetry group and the structure of the classical phase space, giving a strong hint of “superuniversal” KPZ physics in integrable systems invariant under nonabelian symmetries.
COBISS.SI-ID: 42806787
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories. Few are exact and inviolable. I present a new set of methods and sufficient conditions for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations, including diffusivity and the speed of sound. These general techniques combine analytic properties of hydrodynamics and the theory of univalent (complex holomorphic and injective) functions. Particular attention is devoted to bounds relating transport to quantum chaos, which can be established through pole-skipping in theories with holographic duals. Examples of such bounds are shown along with holographic theories that can demonstrate the validity of the conditions involved. I also discuss potential applications of univalence methods to bounds without relation to chaos, such as for example the conformal bound on the speed of sound.
COBISS.SI-ID: 49856003
We found exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations and can exhibit Anderson localization or, surprisingly, ballistic transport at any disorder strength.
COBISS.SI-ID: 3406948