arXiv subjects

Stephen Powell

Publications and source records attributed to Stephen Powell.

36 records · Page 2Linked to original sources

arXiv2015

Scaling dimensions of higher-charge monopoles at deconfined critical points

The classical cubic dimer model has a columnar ordering transition that is continuous and described by a critical Anderson--Higgs theory containing an SU(2)-symmetric complex field minimally coupled to a noncompact U(1) gauge theory. Defects in the dimer constraints correspond to monopoles of the gauge theory, with charge determined by the deviation from unity of the dimer occupancy. By introducing such defects into Monte Carlo simulations of the dimer model at its critical point, we determine the scaling dimensions $y_2 = 1.48\pm0.07$ and $y_3 = 0.20 \pm 0.03$ for the operators corresponding to defects of charge $q=2$ and $3$ respectively. These results, which constitute the first direct determination of the scaling dimensions, shed light on the deconfined critical point of spin-1/2 quantum antiferromagnets, thought to belong to the same universality class. In particular, the positive value of $y_3$ implies that the transition in the JQ model on the honeycomb lattice is of first order.

cond-mat.stat-mech↗

arXiv2015

Ferromagnetic Coulomb phase in classical spin ice

Spin ice is a frustrated magnetic system that at low temperatures exhibits a Coulomb phase, a classical spin liquid with topological order and deconfined excitations. This work establishes the presence of a Coulomb phase with coexisting ferromagnetic order in a microscopic model of classical spin ice subject to uniaxial lattice distortion. General theoretical arguments are presented for the presence of such a phase, and its existence is confirmed using Monte Carlo results. This example is used to illustrate generic properties of spin liquids with magnetic order, including deconfinement of monopoles, signatures in the neutron-scattering structure factor, and critical behavior at phase transitions. An analogous phase, a superfluid with spontaneously broken particle-hole symmetry, is demonstrated in a model of hard-core lattice bosons, related to spin ice through the quantum-classical correspondence.

cond-mat.stat-mech↗

arXiv2013

Critical behavior in the cubic dimer model at nonzero monomer density

We study critical behavior in the classical cubic dimer model (CDM) in the presence of a finite density of monomers. With attractive interactions between parallel dimers, the monomer-free CDM exhibits an unconventional transition from a Coulomb phase to a dimer crystal. Monomers acts as charges (or monopoles) in the Coulomb phase and, at nonzero density, lead to a standard Landau-type transition. We use large-scale Monte Carlo simulations to study the system in the neighborhood of the critical point, and find results in agreement with detailed predictions of scaling theory. Going beyond previous studies of the transition in the absence of monomers, we explicitly confirm the distinction between conventional and unconventional criticality, and quantitatively demonstrate the crossover between the two. Our results also provide additional evidence for the theoretical claim that the transition in the CDM belongs in the same universality class as the deconfined quantum critical point in the SU(2) JQ model.

cond-mat.stat-mech↗

arXiv2012

Confinement of monopoles and scaling theory near unconventional critical points

Conventional ordering transitions, described by the Landau paradigm, are characterized by the symmetries broken at the critical point. Within the constrained manifold occurring at low temperatures in certain frustrated systems, unconventional transitions are possible that defy this type of description. While the critical point exists only in the limit where defects in the constraint are vanishingly rare, unconventional criticality can be observed throughout a broad region of the phase diagram. This work presents a formalism for incorporating the effects of such defects within the framework of scaling theory and the renormalization group, leading to universal results for the critical behavior. The theory is applied to two transitions occurring within a model of spin ice, and the results are confirmed using Monte Carlo simulations. Relevance to experiments, particularly in the spin-ice compounds, is discussed, along with implications for simulations of related transitions, such as the cubic dimer model and the O(3) sigma model with "hedgehog" suppression.

cond-mat.stat-mech↗

arXiv2012

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.

cond-mat.stat-mech↗

arXiv2012

Order by Disorder in Spin-Orbit Coupled Bose-Einstein Condensates

Motivated by recent experiments, we investigate the system of isotropically-interacting bosons with Rashba spin-orbit coupling. At the non-interacting level, there is a macroscopic ground-state degeneracy due to the many ways bosons can occupy the Rashba spectrum. Interactions treated at the mean-field level restrict the possible ground-state configurations, but there remains an accidental degeneracy not corresponding to any symmetry of the Hamiltonian, indicating the importance of fluctuations. By finding analytical expressions for the collective excitations in the long-wavelength limit and through numerical solution of the full Bogoliubov- de Gennes equations, we show that the system condenses into a single momentum state of the Rashba spectrum via the mechanism of order by disorder. We show that in 3D the quantum depletion for this system is small, while the thermal depletion has an infrared logarithmic divergence, which is removed for finite-size systems. In 2D, on the other hand, thermal fluctuations destabilize the system.

cond-mat.quant-gas↗

arXiv2011

Higgs transitions of spin ice

Frustrated magnets such as spin ice exhibit Coulomb phases, where correlations have power-law forms at long distances. Applied perturbations can cause ordering transitions which cannot be described by the usual Landau paradigm, and are instead naturally viewed as Higgs transitions of an emergent gauge theory. Starting from a classical statistical model of spin ice, it is shown that a variety of possible phases and transitions can be described by this approach. Certain cases are identified where continuous transitions are argued to be likely; the predicted critical behavior may be tested in experiments or numerical simulations.

cond-mat.stat-mech↗

arXiv2010

Chiral Rashba spin textures in ultra-cold Fermi gases

Spin-orbit coupling is an important ingredient in many recently discovered phenomena such as the spin-Hall effect and topological insulators. Of particular interest is topological superconductivity, with its potential application in topological quantum computation. The absence of disorder in ultra-cold atomic systems makes them ideal for quantum computation applications, however, the spin-orbit (SO) coupling schemes proposed thus far are experimentally impractical owing to large spontaneous emission rates in the alkali fermions. In this paper, we develop a scheme to generate Rashba SO coupling with a low spontaneous emission extension to a recent experiment. We show that this scheme generates a Fermi surface spin texture for $^{40}\rm{K}$ atoms, which is observable in time-of-flight measurements. The chiral spin texture, together with conventional $s$-wave interactions leads to topological superconductivity and non-Abelian Majorana quasiparticles.

cond-mat.quant-gas↗

arXiv2010

Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field

We consider theoretically the problem of an artificial gauge potential applied to a cold atomic system of interacting neutral bosons in a tight-binding optical lattice. Using the Bose-Hubbard model, we show that an effective magnetic field leads to superfluid phases with simultaneous spatial order, which we analyze using Bogoliubov theory. This gives a consistent expansion in terms of quantum and thermal fluctuations, in which the lowest order gives a Gross-Pitaevskii equation determining the condensate configuration. We apply an analysis based on the magnetic symmetry group to show how the spatial structure of this configuration depends on commensuration between the magnetic field and the lattice. Higher orders describe the quasiparticle excitations, whose spectrum combines the intricacy the Hofstadter butterfly with the characteristic features of the superfluid phase. We use the depletion of the condensate to determine the range of validity of our approximations and also to find an estimate for the onset of the Mott insulator phase. Our theory provides concrete experimental predictions, for both time-of-flight imagery and Bragg spectroscopy.

cond-mat.quant-gas↗

arXiv2010

Interacting Hofstadter spectrum of atoms in an artificial gauge field

Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements. The theory also provides an estimate of the critical interaction strength at the transition to the Mott insulator phase.

cond-mat.quant-gas↗

arXiv2009

Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model

We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition that results, from a superfluid to a Mott insulator at fractional filling, belongs to a class that cannot be described within the Landau-Ginzburg-Wilson paradigm. Using a second mapping, to a dual model of vortices, we show that the long-wavelength physics near the transition is described by a U(1) gauge theory with SU(2) matter fields.

cond-mat.stat-mech↗

arXiv2009

Magnetic phases and transitions of the two-species Bose-Hubbard model

A model of two-species bosons moving on the sites of a lattice is studied at nonzero temperature, focusing on magnetic order and superfluid-insulator transitions. Firstly, Landau theory is used to find the general structure of the phase diagram, and in particular to demonstrate the presence of first-order transitions and hysteresis in the vicinity of a multicritical point. Secondly, an explicit thermodynamic phase diagram is calculated using an approach based on a field-theoretical description of the Bose-Hubbard model, which incorporates the crucial effects of particle-number fluctuations. The maximum transition temperature to a magnetically ordered Mott insulator is found to be limited by the presence of the superfluid phase.

cond-mat.stat-mech↗

arXiv2008

SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.

cond-mat.stat-mech↗

arXiv2008

Classical-Quantum Mappings for Geometrically Frustrated Systems: Spin Ice in a [100] Field

Certain classical statistical systems with strong local constraints are known to exhibit Coulomb phases, where long-range correlation functions have power-law forms. Continuous transitions from these into ordered phases cannot be described by a naive application of the Landau-Ginzburg-Wilson theory, since neither phase is thermally disordered. We present an alternative approach to a critical theory for such systems, based on a mapping to a quantum problem in one fewer spatial dimensions. We apply this method to spin ice, a magnetic material with geometrical frustration, which exhibits a Coulomb phase and a continuous transition to an ordered state in the presence of a magnetic field applied in the [100] direction.

cond-mat.stat-mech↗

arXiv2007

Spin dynamics across the superfluid-insulator transition of spinful bosons

Bosons with non-zero spin exhibit a rich variety of superfluid and insulating phases. Most phases support coherent spin oscillations, which have been the focus of numerous recent experiments. These spin oscillations are Rabi oscillations between discrete levels deep in the insulator, while deep in the superfluid they can be oscillations in the orientation of a spinful condensate. We describe the evolution of spin oscillations across the superfluid-insulator quantum phase transition. For transitions with an order parameter carrying spin, the damping of such oscillations is determined by the scaling dimension of the composite spin operator. For transitions with a spinless order parameter and gapped spin excitations, we demonstrate that the damping is determined by an associated quantum impurity problem of a localized spin excitation interacting with the bulk critical modes. We present a renormalization group analysis of the quantum impurity problem, and discuss the relationship of our results to experiments on ultracold atoms in optical lattices.

cond-mat.str-el↗

arXiv2006

Excited state spectra at the superfluid-insulator transition out of paired condensates

We describe gapped single-particle and collective excitations across a superfluid to insulator quantum phase transition of particles (bosons or fermions) in a periodic potential, with an even number of particles per unit cell. We demonstrate that the dynamics is controlled by a quantum impurity problem of a localized particle interacting with the bulk critical modes. Critical exponents are determined by a renormalization group analysis. We discuss applications to spin oscillations of ultracold atoms in optical lattices, and to the electronic phases in the cuprate and related compounds.

cond-mat.str-el↗

arXiv2005

Depletion of the Bose-Einstein condensate in Bose-Fermi mixtures

We describe the properties of a mixture of fermionic and bosonic atoms, as they are tuned across a Feshbach resonance associated with a fermionic molecular state. Provided the number of fermionic atoms exceeds the number of bosonic atoms, we argue that there is a critical detuning at which the Bose-Einstein condensate (BEC) is completely depleted. The phases on either side of this quantum phase transition can also be distinguished by the distinct Luttinger constraints on their Fermi surfaces. In both phases, the total volume enclosed by all Fermi surfaces is constrained by the total number of fermions. However, in the phase without the BEC, which has two Fermi surfaces, there is a _second_ Luttinger constraint: the volume enclosed by one of the Fermi surfaces is constrained by the total number of_bosons_, so that the volumes enclosed by the two Fermi surfaces are separately conserved. The phase with the BEC may have one or two Fermi surfaces, but only their total volume is conserved. We obtain the phase diagram as a function of atomic parameters and temperature, and describe critical fluctuations in the vicinity of all transitions. We make quantitative predictions valid for the case of a narrow Feshbach resonance, but we expect the qualitative features we describe to be more generally applicable. As an aside, we point out intriguing connections between the BEC depletion transition and the transition to the fractionalized Fermi liquid in Kondo lattice models.

cond-mat.stat-mech↗

arXiv2003

Quench dynamics across quantum critical points

We study the quantum dynamics of a number of model systems as their coupling constants are changed rapidly across a quantum critical point. The primary motivation is provided by the recent experiments of Greiner et al. (Nature 415, 39 (2002)) who studied the response of a Mott insulator of ultracold atoms in an optical lattice to a strong potential gradient. In a previous work (cond-mat/0205169), it had been argued that the resonant response observed at a critical potential gradient could be understood by proximity to an Ising quantum critical point describing the onset of density wave order. Here we obtain numerical results on the evolution of the density wave order as the potential gradient is scanned across the quantum critical point. This is supplemented by studies of the integrable quantum Ising spin chain in a transverse field, where we obtain exact results for the evolution of the Ising order correlations under a time-dependent transverse field. We also study the evolution of transverse superfluid order in the three dimensional case. In all cases, the order parameter is best enhanced in the vicinity of the quantum critical point.

cond-mat.str-el↗