Unitarity in periodic potentials: a renormalization group analysis

We explore the universal properties of interacting fermionic lattice systems, mostly focusing on the development of pairing correlations from attractive interactions. Using renormalization group we identify a large number of fixed points and show that they correspond to resonant scattering in multiple channels. Pairing resonances in finite-density band insulators occur between quasiparticles and quasiholes living at different symmetry-related wavevectors in the Brillouin zone. This allows a BCS-BEC crossover interpretation of both Cooper and particle-hole pairing. We show that in two dimensions the run-away flows of relevant attractive interactions lead to charged-boson-dominated low energy dynamics in the insulating states, and superfluid transitions in bosonic mean-field or XY universality classes. Analogous phenomena in higher dimensions are restricted to the strong coupling limit, while at weak couplings the transition is in the pair-breaking BCS class. The models discussed here can be realized with ultra-cold gases of alkali atoms tuned to a broad Feshbach resonance in an optical lattice, enabling experimental studies of pairing correlations in insulators, especially in their universal regimes. In turn, these simple and tractable models capture the emergence of fluctuation-driven superconducting transitions in fermionic systems, which is of interest in the context of high temperature superconductors.Comment: 16 pages, 6 figures, published versio

Unconventional Quantum Critical Points

In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional quantum critical points will be discussed: (1). The transition between topological order and semiclassical spin ordered phase; (2). The transition between topological order and valence bond solid phase; (3). The direct second order transition between different competing orders. We focus on the field theory and universality class of these unconventional quantum critical points. Relation of these quantum critical points with recent numerical simulations and experiments on quantum frustrated magnets are also discussed.Comment: 28 pages, 6 figures. Review article for Int. J. Mod. Phys.

Energy transport in strongly disordered superconductors and magnets

We develop an analytical theory for quantum phase transitions driven by disorder in magnets and superconductors. We study these transitions with a cavity approximation which becomes exact on a Bethe lattice with large branching number. We find two different disordered phases, characterized by very different relaxation rates, which both exhibit strong inhomogeneities typical of glassy physics.Comment: 4 pages, 1 figur

Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets: I. Theory

We consider theoretically the effects of an applied uniform magnetic field on the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya layered quantum Heisenberg antiferromagnets. The first case is relevant for systems such as the two-dimensional square lattice antiferromagnet Sr(2)CuO(2)Cl(2), while the later is known to be relevant to the physics of the layered orthorhombic antiferromagnet La(2)CuO(4). We first establish the correspondence betwenn the low-energy spectrum obtained within the anisotropic non-linear sigma model and by means of the spin-wave approximation for a standard easy-axis antiferromagent. Then, we focus on the field-theory approach to calculate the magnetic field dependence of the magnon gaps and spectral intensities for magnetic fields applied along the three possible crystallographic directions. We discuss the various possible ground states and their evolution with temperature for the different field orientations, and the occurrence of spin-flop transitions for fields perpendicular to the layers (transverse fields) as well as for fields along the easy axis (longitudinal fields). Measurements of the one-magnon Raman spectrum in Sr(2)CuO(2)Cl(2) and La(2)CuO(4) and a comparison between the experimental results and the predictions of the present theory will be reported in part II of this research work [L. Benfatto et al., cond-mat/0602664].Comment: 21 pages, 11 figures, final version. Part II of the present work is presented in cond-mat/060266

Correlated bosons in a one-dimensional optical lattice: Effects of the trapping potential and of quasiperiodic disorder

We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.Comment: Accepted for publication in PR

Universal monopole scaling near transitions from the Coulomb phase

Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge theory becomes confining, provide examples of unconventional criticality. This work studies the behavior at nonzero monopole density near such transitions, using scaling theory to arrive at universal expressions for the crossover phenomena. For a particular transition in spin ice, quantitative predictions are made through a duality mapping to the XY model, and confirmed using Monte Carlo simulations.Comment: 4.5 pages, 4 figure

Nonequilibrium dynamical renormalization group: Dynamical crossover from weak to infinite randomness in the transverse-field Ising chain

In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational invariant and disordered systems. As a concrete application we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.Comment: 15 pages, 4 figures, extended presentation, version as publishe

Quantum phases of interacting phonons in ion traps

The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. Besides that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, like models with attractive or site--dependent phonon-phonon interactions.Comment: 10 page

Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one-deimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure

Exact results for quench dynamics and defect production in a two-dimensional model

We show that for a d-dimensional model in which a quench with a rate \tau^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/\tau^{m\nu/(z\nu +1)}, where \nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m=\nu=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.Comment: 4 pages including 4 figures; generalized the discussion of the defect density scaling to the case of arbitrary critical exponents, and added some references; this version will appear in Physical Review Letter