Leonid P. Pryadko

Supersolids versus Phase Separation in Two-Dimensional Lattice Bosons

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.

Fault tolerance of quantum low-density parity check codes with sublinear distance scaling

Quantum low-density parity check (LDPC) codes such as generalized toric codes with finite rate suggested by Tillich and Zémor offer an alternative route for quantum computation. Here, we study LDPC codes and show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, has a finite error threshold. Based on that, we conclude that quantum LDPC codes, for sufficiently large quantum computers, can offer an advantage over the toric codes.

Tight lower bound for percolation threshold on an infinite graph.

We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graphs adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.

Fluctuation-induced forces between inclusions in a fluid membrane under tension

We develop an exact method to calculate thermal Casimir forces between inclusions of arbitrary shapes and separation, embedded in a fluid membrane whose fluctuations are governed by the combined action of surface tension, bending modulus, and Gaussian rigidity. Each objects shape and mechanical properties enter only through a characteristic matrix, a static analog of the scattering matrix. We calculate the Casimir interaction between two elastic disks embedded in a membrane. In particular, we find that at short separations the interaction is strong and independent of surface tension.

Quantum Phase Slips in the Presence of Finite-Range Disorder

To study the effect of disorder on quantum phase slips (QPSs) in superconducting wires, we consider the plasmon-only model where disorder can be incorporated into a first-principles instanton calculation. We consider weak but general finite-range disorder and compute the form factor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance Z of the wire and with a superconductor-insulator transition at Z = 6.5 k. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.

Incipient Order in the t-J Model at High Temperatures

We analyze the high-temperature behavior of the susceptibilities towards a number of possible ordered states in the t-J-V model using the high-temperature series expansion. From all diagrams with up to ten edges, reliable results are obtained down to temperatures of order J, or (with some optimism) to J/2. In the unphysical regime, t<J, large superconducting susceptibilities are found which, moreover, increase with decreasing temperatures, but for t>J, these susceptibilities are small and decreasing with decreasing temperature; this suggests that the t-J model does not support high-temperature superconductivity. We also find modest evidence of a tendency toward nematic and d-density wave orders.

Improved quantum hypergraph-product LDPC codes

We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Zémor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal single-qubit-encoding toric codes with block length n = t2 + (t+1)2 and distance d = 2t + 1, t = 1, 2, ... We also suggest several related algebraic constructions which increase the rate of the existing hypergraph-product codes by up to four times.

Attachment and detachment rate distributions in deep-bed filtration

We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field description in which the attachment and detachment processes are characterized by an entire spectrum of rate constants, ranging from shallow traps which mostly account for hydrodynamic dispersivity, all the way to the permanent traps associated with physical straining. The model has an analytical solution which allows analysis of its properties including the long-time asymptotic behavior and the profile of the deposition curves. Furthermore, the model gives rise to a filtering front whose structure, stability, and propagation velocity are examined. Based on these results, we propose an experimental protocol to determine the parameters of the model.

Topological doping and the stability of stripe phases

We analyze the properties of a general Ginzburg-Landau free energy with competing order parameters, long-range interactions, and global constraints (e.g., a fixed value of a total {open_quotes}charge{close_quotes}) to address the physics of stripe phases in underdoped high-T{sub c} and related materials. For a local free energy limited to quadratic terms of the gradient expansion, only uniform or phase-separated configurations are thermodynamically stable. {open_quotes}Stripe{close_quotes} or other nonuniform phases can be stabilized by long-range forces, but can only have nontopological (in-phase) domain walls where the components of the antiferromagnetic order parameter never change sign, and the periods of charge and spin-density waves coincide. The {ital antiphase} domain walls observed experimentally require physics on an intermediate length scale, and they are absent from a model that involves only long-distance physics. Dense stripe phases can be stable even in the absence of long-range forces, but domain walls always attract at large distances; i.e., there is a ubiquitous tendency to phase separation at small doping. The implications for the phase diagram of underdoped cuprates are discussed. {copyright} {ital 1999} {ital The American Physical Society}

Scalable Design of Tailored Soft Pulses for Coherent Control

We present a scalable scheme to design optimized soft pulses and pulse sequences for coherent control of interacting quantum many-body systems. The scheme is based on the cluster expansion and the time-dependent perturbation theory implemented numerically. This approach offers a dramatic advantage in numerical efficiency, and it is also more convenient than the commonly used Magnus expansion, especially when dealing with higher-order terms. We illustrate the scheme by designing 2nd-order self-refocusing pi pulses and a 6th-order 8-pulse refocusing sequence for a chain of qubits with nearest-neighbor couplings. We also discuss the performance of soft-pulse refocusing sequences in suppressing decoherence due to low-frequency environment.