Ground and thermal state properties of model spin systems

Araceli Venegas‐Gomez, Anton S. Buyskikh, Johannes Schachenmayer +2 more

The microscopic control available over cold atoms in optical lattices has opened new opportunities to study the properties of quantum spin models. While a lot of attention is focused on experimentally realizing ground or thermal states via adiabatic loading, it would often be more straightforward to prepare specific simple product states and to probe the properties of interacting spins by observing their dynamics. We explore this possibility for spin-1/2 and spin-1 models that can be realized with bosons in optical lattices, and which exhibit $\mathit{XY}$-ferromagnetic (or counterflow spin-superfluid) phases. We consider the dynamics of initial spin-rotated states corresponding to a mean-field version of the phases of interest. Using matrix product state methods in one dimension, we compute both nonequilibrium dynamics and ground and thermal states for these systems. We compare and contrast their behavior in terms of correlation functions and induced spin currents, which should be directly observable with current experimental techniques. We find that although spin correlations decay substantially at large distances and on long timescales, for induction of spin currents, the rotated states behave similarly to the ground states on experimentally observable timescales.

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Masanori Ohya, Dėnes Petz

Pancotti, N., Giudice, G., J. I. Cirac +2 more

We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically-constrained models of classical glasses. Through a combination of analytics, exact diagonalization and tensor-network methods we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of non-thermal states which become exact finite-energy-density eigenstates in the large-size limit, as expected for a true phase transition. A ``super-spin'' generalization allows us to find a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that} many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the non-thermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and non-ergodicity more generally in disorder-free systems with constraints and we give numerical evidence that these results may be extended to two dimensional systems.

Takuma Nishimura, M. Katsumura, T. Morita +3 more

Gaurav Harsha

Wave function methods have offered a robust, systematically improvable means to study the ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogs of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space. Approximating every state in the Hilbert space is an impossible task. Besides, excited-state theories are not as well studied as ground-state ones. In this thesis, we overcome these difficulties by employing thermofield dynamics, a theory that allows the purification of the ensemble density matrix and constructs a pure wave function that encodes the equilibrium thermal behavior of the system. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we develop a framework to extend ground-state wave function theories to non-zero temperatures. We discuss explicit formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of fermions in the grand canonical ensemble. For fermions in the canonical ensemble, we present mean-field, configuration interaction, and perturbation theories. We also discuss thermal mean-field, configuration interaction, and coupled cluster formalisms for \SU systems. To assess the quality of these approximations, we study both model and small atomic and molecular as benchmark electronic problems while comparing against exact results. For spins, we use the Lipkin-Meshkov-Glick and the one-dimensional transverse field Ising models as our reference systems. Indeed, the thermal methods perform reasonably well while merely adding a prefactor to the computational cost. They also inherit all the properties, good or bad, from their ground-state counterparts, signifying the robustness of our formalism.