Andreas M. Läuchli

Quench Dynamics and Nonequilibrium Phase Diagram of the Bose-Hubbard Model

We investigate the time evolution of correlations in the Bose-Hubbard model following a quench from the superfluid to the Mott insulator. For large values of the final interaction strength the system approaches a distinctly nonequilibrium steady state that bears strong memory of the initial conditions. In contrast, when the final interaction strength is comparable to the hopping, the correlations are rather well approximated by those at thermal equilibrium. The existence of two distinct nonequilibrium regimes is surprising given the nonintegrability of the Bose-Hubbard model. We relate this phenomenon to the role of quasiparticle interactions in the Mott insulator.

Effect of rare fluctuations on the thermalization of isolated quantum systems.

We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In particular, we investigate the prerequisites for thermalization, focusing on the statistical properties of the time-averaged density matrix and of the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the microcanonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some nonintegrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two scenarios for thermalization.

Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model

We investigate the spreading of information in a one-dimensional Bose-Hubbard system after a sudden parameter change. In particular, we study the time evolution of correlations and entanglement following a quench. The investigated quantities show a light-cone-like evolution, i.e. the spreading with a finite velocity. We discuss the relation of this velocity to other characteristic velocities of the system, like the sound velocity. The entanglement is investigated using two different measures, the von Neumann entropy and mutual information. Whereas the von Neumann entropy grows rapidly with time the mutual information between two small subsystems can decrease as well after an initial increase. Additionally we show that the static von Neumann entropy characterizes the location of the quantum phase transition.

Realizing Fractional Chern Insulators in Dipolar Spin Systems

Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the ν = 1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultracold polar molecules trapped in a deep optical lattice. With the motion of the molecules pinned, under certain conditions, these rotational excitations form a fractional Chern insulating state. We present a detailed experimental blueprint for its realization and demonstrate that the implementation is consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications.

Emergent multipolar spin correlations in a fluctuating spiral: The frustrated ferromagnetic spin-1/2 Heisenberg chain in a magnetic field

We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J(1)-J(2) chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states toward spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional S=1/2 quantum magnets in a magnetic field.

Plaquette valence-bond crystal in the frustrated Heisenberg quantum antiferromagnet on the square lattice

Using both exact diagonalizations and diagonalizations in a subset of short-range valence-bond singlets, we address the nature of the groundstate of the Heisenberg spin-

Orbital Currents in Extended Hubbard Models of High-T c Cuprate Superconductors

1∕2

Frustrated three-leg spin tubes : From spin 1/2 with chirality to spin 3/2

antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (

Disentangling entanglement spectra of fractional quantum Hall states on torus geometries.

{J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}

Phase diagram of a spin ladder with cyclic four-spin exchange

model). A detailed comparison of the two approaches reveals a region along the line