Michael Kolodrubetz

Observation of topological transitions in interacting quantum circuits

Topology, with its abstract mathematical constructs, often manifests itself in physics and has a pivotal role in our understanding of natural phenomena. Notably, the discovery of topological phases in condensed-matter systems has changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and, as a result, are inadequate for studying the topology of physical systems at a fundamental level. Here we employ the exquisite control afforded by state-of-the-art superconducting quantum circuits to investigate topological properties of various quantum systems. The essence of our approach is to infer geometric curvature by measuring the deflection of quantum trajectories in the curved space of the Hamiltonian. Topological properties are then revealed by integrating the curvature over closed surfaces, a quantum analogue of the Gauss–Bonnet theorem. We benchmark our technique by investigating basic topological concepts of the historically important Haldane model after mapping the momentum space of this condensed-matter model to the parameter space of a single-qubit Hamiltonian. In addition to constructing the topological phase diagram, we are able to visualize the microscopic spin texture of the associated states and their evolution across a topological phase transition. Going beyond non-interacting systems, we demonstrate the power of our method by studying topology in an interacting quantum system. This required a new qubit architecture that allows for simultaneous control over every term in a two-qubit Hamiltonian. By exploring the parameter space of this Hamiltonian, we discover the emergence of an interaction-induced topological phase. Our work establishes a powerful, generalizable experimental platform to study topological phenomena in quantum systems.

Ergodic dynamics and thermalization in an isolated quantum system

The realization of a quantum kicked top provides evidence for ergodic dynamics and thermalization in a small quantum system consisting of three superconducting qubits.

Nonequilibrium dynamic critical scaling of the quantum Ising chain.

We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields.

We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.

The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem.

The sign problem in full configuration interaction quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper, we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.M.H. Kolodrubetz, 2 J.S. Spencer, 4 B.K. Clark, 5, 6 and W.M.C. Foulkes Department of Physics, Princeton University, Princeton, NJ 08544, U.S.A. Department of Physics, Boston University, Boston, MA 02215, U.S.A. Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, U.K. Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, U.K. Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, U.S.A. Station Q, Microsoft Research, Santa Barbara, CA 93106, U.S.A.

Partial node configuration-interaction Monte Carlo as applied to the Fermi polaron

Finding the ground state of a fermionic Hamiltonian using quantum Monte Carlo is a very difficult problem, due to the Fermi sign problem. While still scaling exponentially, full configurationinteraction Monte Carlo (FCI-QMC) mitigates some of the exponential variance by allowing annihilation of noise – whenever two walkers arrive at the same configuration with opposite signs, they are removed from the simulation. While FCI-QMC has been quite successful for quantum chemistry problems, its application to problems in condensed systems has been limited. In this paper, we apply FCI-QMC to the Fermi polaron problem, which provides an ideal test-bed for improving the algorithm. In its simplest form, FCI-QMC is unstable for even a fairly small system sizes. However, with a series of algorithmic improvements, we are able to significantly increase its effectiveness. We modify fixed node QMC to work in these systems, introduce a well chosen importance sampled trial wave function, a partial node approximation, and a variant of released node. Finally, we develop a way to perform FCI-QMC directly in the thermodynamic limit

Nonequilibrium dynamics of bosonic Mott insulators in an electric field

We study the nonequilibrium dynamics of one-dimensional Mott-insulating bosons in the presence of a tunable effective electric field e which takes the system across a quantum critical point separating a disordered and a translation symmetry broken ordered phase. We provide an exact numerical computation of the residual energy Q, the log fidelity F, the defect density D/L, and the order parameter correlation function for a linear-in-time variation of E with a rate v. We discuss the temporal and spatial variation of these quantities for a range of v and for finite system sizes as relevant to realistic experimental setups [ J. Simon et al. Nature (London) 472 307 (2011)]. We show that in finite-sized systems Q, F, and D obey Kibble-Zurek scaling, and suggest further experiments within this setup to test our theory.

Floquet Dynamics of Boundary-Driven Systems at Criticality

A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes, depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model and demonstrate universality by adding nonintegrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.

Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementations

In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field

Absence of Thermalization in Finite Isolated Interacting Floquet Systems

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