Mott insulators in strong electric fields

Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference

Monte Carlo Simulations with Indefinite and Complex-Valued Measures

A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. Exactly solvable, one-dimensional Ising models with complex temperature and complex activity illustrate the considerable improvements and the workability of the new method even when the crude one fails.Comment: 10 A4 pages, postscript (140K), UM-P-93-7

High resolution studies of low-energy electron attachment to SF5Cl: Product anions and absolute cross sections

Low energy electron attachment to SF$_5$Cl was studied at high energy resolution by mass spectrometric detection of the product anions. Two variants of the laser photoelectron attachment (LPA) technique (Kaiserslautern) were used for determining the threshold behaviour of the yield for SF$_5^-$ formation at about 1 meV resolution, and to investigate the relative cross sections for Cl$^-$, FCl$^-$, and SF$_5^-$ formation towards higher energies (up to 1 eV) at about 20 meV resolution. Thermal swarm measurements (Birmingham) were used to place the relative LPA cross sections on an absolute scale. A trochoidal electron monochromator (Innsbruck) was used for survey measurements of the relative cross sections for the different product anions over the energy range of 0-14 eV with a resolution of 0.30 eV. Combined with earlier beam data (taken at Berlin, J. Chem. Phys. 88 (1988) 149), the present experimental results provide a detailed set of partial cross sections for anion formation in low-energy electron collisions with SF$_5$Cl

Exact Zeros of the Partition Function for a Continuum System with Double Gaussian Peaks

We calculate the exact zeros of the partition function for a continuum system where the probability distribution for the order parameter is given by two asymmetric Gaussian peaks. When the positions of the two peaks coincide, the two separate loci of zeros which used to give first-order transition touch each other, with density of zeros vanishing at the contact point on the positive real axis. Instead of the second-order transition of Ehrenfast classification as one might naively expect, one finds a critical behavior in this limit.Comment: 13 pages, 6 figures, revtex, minor changes in fig.2, to be published in Physical Review

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.Comment: 14 pages, 8 figure

Quantum field theory of metallic spin glasses

We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains reference to related work in cond-mat/950412

Decay of the metastable phase in d=1 and d=2 Ising models

We calculate perturbatively the tunneling decay rate $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.Comment: 4 pages, REVTe

1D Potts, Yang-Lee Edges and Chaos

It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model. In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-Lee zeroes no longer lie on the unit circle in the complex z = exp (h) plane, but their locus is still reproduced by the boundary of the chaotic region in the logistic map.Comment: 6 pages, no figure

The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.Comment: 19 pages, 30 figure

The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur