Valence bond solid order near impurities in two-dimensional quantum antiferromagnets

Recent scanning tunnelling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states which are centered on a Cu-O-Cu bond (Kohsaka et. al., cond-mat/0703309). As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered Neel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: i) local modulation in the exchange constants, and ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The `boundary' critical theory for these classes is developed: in the second class we find a `VBS pinwheel' around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.Comment: 41 pages, 6 figures; (v2) Minor changes in terminology, added reference

Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La$_{2}$Cu$_{1-p}$(Zn,Mg)$_{p}$O$_{4}$. Our results are also relevant for disordered interacting boson systems.Comment: 4 pages, 3 eps figures, final version, as publishe

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

Creating maximally entangled atomic states in a Bose-Einstein condensate

We propose a protocol to create maximally entangled pairs, triplets, quartiles, and other clusters of Bose condensed atoms starting from a condensate in the Mott insulator state. The essential element is to drive single atom Raman transitions using laser pulses. Our scheme is simple, efficient, and can be readily applied to the recent experimental system as reported by Greiner {\it et al.} [ Nature {\bf 413}, 44 (2002)].Comment: 4 pages, 2 figures. revised version as to be publishe

Topological Winding and Unwinding in Metastable Bose-Einstein Condensates

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of grey solitons, or density notches, which serve as an experimental signature of this phenomenon.Comment: 4 pages, 3 figure

Quench induced Mott insulator to superfluid quantum phase transition

Mott insulator to superfluid quenches have been used by recent experiments to generate exotic superfluid phases. While the final Hamiltonian following the sudden quench is that of a superfluid, it is not a priori clear how close the final state of the system approaches the ground state of the superfluid Hamiltonian. To understand the nature of the final state we calculate the temporal evolution of the momentum distribution following a Mott insulator to superfluid quench. Using the numerical infinite time-evolving block decimation approach and the analytical rotor model approximation we establish that the one and two dimensional Mott insulators following the quench equilibriate to thermal states with spatially short-ranged coherence peaks in the final momentum distribution and therefore are not strict superfluids. However, in three dimensions we find a divergence in the momentum distribution indicating the emergence of true superfluid order.Comment: 4.2 pages, 3 Figure

Large-Scale Schr\"odinger-Cat States and Majorana Bound States in Coupled Circuit-QED Systems

We have studied the low-lying excitations of a chain of coupled circuit-QED systems, and report several intriguing properties of its two nearly degenerate ground states. The ground states are Schr\"odinger cat states at a truly large scale, involving maximal entanglement between the resonator and the qubit, and are mathematically equivalent to Majorana bound states. With a suitable design of physical qubits, they are protected against local fluctuations and constitute a non-local qubit. Further, they can be probed and manipulated coherently by attaching an empty resonator to one end of the circuit-QED chain.Comment: 5 pages; 2 figures; incorrect references corrected; typos correcte

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

Boson Core Compressibility

Strongly interacting atoms trapped in optical lattices can be used to explore phase diagrams of Hubbard models. Spatial inhomogeneity due to trapping typically obscures distinguishing observables. We propose that measures using boson double occupancy avoid trapping effects to reveal key correlation functions. We define a boson core compressibility and core superfluid stiffness in terms of double occupancy. We use quantum Monte Carlo on the Bose-Hubbard model to empirically show that these quantities intrinsically eliminate edge effects to reveal correlations near the trap center. The boson core compressibility offers a generally applicable tool that can be used to experimentally map out phase transitions between compressible and incompressible states.Comment: 11 pages, 11 figure

Weyl corrections to holographic conductivity

For conformal field theories which admit a dual gravitational description in anti-de Sitter space, electrical transport properties, such as conductivity and charge diffusion, are determined by the dynamics of a U(1) gauge field in the bulk and thus obey universality relations at the classical level due to the uniqueness of the Maxwell action. We analyze corrections to these transport parameters due to higher-dimension operators in the bulk action, beyond the leading Maxwell term, of which the most significant involves a coupling to the bulk Weyl tensor. We show that the ensuing corrections to conductivity and the diffusion constant break the universal relation with the U(1) central charge observed at leading order, but are nonetheless subject to interesting bounds associated with causality in the boundary CFT.Comment: 15 pages, v2: references adde