arXiv subjects

R. G. Melko

Publications and source records attributed to R. G. Melko.

17 recordsLinked to original sources

arXiv2016

Entanglement area law in superfluid $^4$He

Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic numerical simulations of superfluid $^4$He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an "entanglement equation of state" showing how it depends on the density of the superfluid.

cond-mat.other↗

arXiv2016

Spatial entanglement entropy in the ground state of the Lieb-Liniger model

We consider the entanglement between two spatial subregions in the Lieb-Liniger model of bosons in one spatial dimension interacting via a contact interaction. Using ground state path integral quantum Monte Carlo we numerically compute the Rényi entropy of the reduced density matrix of the subsystem as a measure of entanglement. Our numerical algorithm is based on a replica method previously introduced by the authors, which we extend to efficiently study the entanglement of spatial subsystems of itinerant bosons. We confirm a logarithmic scaling of the Rényi entropy with subsystem size that is expected from conformal field theory, and compute the non-universal subleading constant for interaction strengths ranging over two orders of magnitude. In the strongly interacting limit, we find agreement with the known free fermion result.

cond-mat.quant-gas↗

arXiv2015

Entangling qubit registers via many-body states of ultracold atoms

Inspired by the experimental measurement of the Renyi entanglement entropy in a lattice of ultracold atoms by Islam et al., [Nature 528, 77 (2015)] we propose a method to entangle two spatially-separated qubits using the quantum many-body state as a resource. Through local operations accessible in an experiment, entanglement is transferred to a qubit register from atoms at the ends of a one-dimensional chain. We compute the operational entanglement, which bounds the entanglement physically transferable from the many-body resource to the register, and discuss a protocol for its experimental measurement. Finally, we explore measures for the amount of entanglement available in the register after transfer, suitable for use in quantum information applications.

cond-mat.quant-gas↗

arXiv2014

A path integral Monte Carlo method for Rényi entanglement entropies

We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability and interactions. We present proof-of-principle calculations, and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large scale many-body systems of interacting bosons.

cond-mat.quant-gas↗

arXiv2014

Particle entanglement in continuum many-body systems via quantum Monte Carlo

Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the Rényi entanglement entropies on a particle bipartition, with general applicability to continuum Hamiltonians via path integral Monte Carlo methods. Via direct simulations of interacting bosons in one spatial dimension, we confirm a logarithmic scaling of the single-particle entanglement entropy with the number of particles in the system. The coefficient of this logarithmic scaling increases with interaction strength, saturating to unity in the strongly interacting limit. Additionally, we show that the single-particle entanglement entropy is bounded by the condensate fraction, suggesting a practical route towards its measurement in future experiments.

cond-mat.quant-gas↗

arXiv2013

Non-monotonic residual entropy in diluted spin ice: a comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results

Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, have been the subject of much interest for over the past fifteen years. Their low temperature strongly correlated state can be mapped onto the proton disordered state of common water ice and, consequently, spin ices display the same low temperature residual Pauling entropy as water ice. Interestingly, it was found in a previous study [X. Ke {\it et. al.} Phys. Rev. Lett. {\bf 99}, 137203 (2007)] that, upon dilution of the magnetic rare-earth ions (Dy^{3+} and Ho^{3+}) by non-magnetic Yttrium (Y^{3+}) ions, the residual entropy depends {\it non-monotonically} on the concentration of Y^{3+} ions. In the present work, we report results from Monte Carlo simulations of site-diluted microscopic dipolar spin ice models (DSIM) that account quantitatively for the experimental specific heat measurements, and thus also for the residual entropy, as a function of dilution, for both Dy2Ti2O7 and Ho2Ti2O7. The main features of the dilution physics displayed by the magnetic specific heat data are quantitatively captured by the diluted DSIM up to, and including, 85% of the magnetic ions diluted (x=1.7). The previously reported departures in the residual entropy between Dy2Ti2O7 versus Ho2Ti2O7, as well as with a site-dilution variant of Pauling's approximation, are thus rationalized through the site-diluted DSIM. For 90% (x=1.8) and 95% (x=1.9) of the magnetic ions diluted, we find a significant discrepancy between the experimental and Monte Carlo specific heat results. We discuss some possible reasons for this disagreement.

cond-mat.stat-mech↗

arXiv2010

Continuous thermal melting of a two-dimensional Abrikosov vortex solid

We examine the question of thermal melting of the triangular Abrikosov vortex solid in two-dimensional superconductors or neutral superfluids. We introduce a model, which combines lowest Landau level (LLL) projection with the magnetic Wannier basis to represent degenerate eigenstates in the LLL. Solving the model numerically via large-scale Monte Carlo simulations, we find clear evidence for a continuous melting transition, in perfect agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory and with recent experiments.

cond-mat.supr-con↗

arXiv2006

A striped supersolid phase and the search for deconfined quantum criticality in hard-core bosons on the triangular lattice

Using large-scale quantum Monte Carlo simulations we study bosons hopping on a triangular lattice with nearest (V) and next-nearest (V') neighbor repulsive interactions. In the limit where V=0 but V' is large, we find an example of an unusual period-three striped supersolid state that is stable at 1/2-filling. We discuss the relationship of this state to others on the rich ground-state phase diagram, which include a previously-discovered nearest-neighbor supersolid, a uniform superfluid, as well as several Mott insulating phases. We study several superfluid- and supersolid-to-Mott phase transitions, including one proposed by a recent phenomenological dual vortex field theory as a candidate for an exotic deconfined quantum critical point. We find no examples of unconventional quantum criticality among any of the interesting phase transitions in the model.

cond-mat.str-el↗

arXiv2006

Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice

Using large scale quantum Monte Carlo simulations and dual vortex theory we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest neighbor repulsion. In contrast to the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half-filling, two novel solid phases emerge at densities $ρ=1/3$ and $ρ=2/3$. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.

cond-mat.str-el↗

arXiv2005

Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice

We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half-filling, we demonstrate that superfluidity survives for arbitrarily large repulsion, and that diagonal solid order emerges in the strongly correlated regime from an order-by-disorder mechanism. This is thus an unusual example of a stable supersolid phase of hard-core lattice bosons at a commensurate filling.

cond-mat.str-el↗

arXiv2004

Persistent superfluid phase in a three-dimensional quantum XY model with ring exchange

We present quantum Monte Carlo simulation results on a quantum S=1/2 XY model with ring exchange (the J-K model) on a three-dimensional simple cubic lattice. We first characterize the ground state properties of the pure XY model, obtaining estimations for the energy, spin stiffness and spin susceptibility at T=0 in the superfluid phase. With the ring exchange, we then present simulation data on small lattices which suggests that the superfluid phase persists to very large values of the ring exchange K, without signatures of a phase transition. We comment on the consequences of this result for the search for various exotic phases in three dimensions.

cond-mat.str-el↗

arXiv2004

Neutron Scattering Investigation of the Spin Ice State in Dy2Ti2O7

Dy2Ti2O7 has been advanced as an ideal spin ice. We present a neutron scattering investigation of a sample of 162Dy2Ti2O7. The scattering intensity has been mapped in zero applied field in the hhl and hk0 planes at temperatures between 0.05 K and 20 K. The measured diffuse scattering (in the static approximation) has been compared to that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.

cond-mat.dis-nn↗

arXiv2004

Aspect-ratio dependence of the spin stiffness of a two-dimensional XY model

We calculate the superfluid stiffness of 2D lattice hard-core bosons at half-filling (equivalent to the S=1/2 XY-model) using the squared winding number quantum Monte Carlo estimator. For L_x x L_y lattices with aspect ratio L_x/L_y=R, and L_x,L_y -> infinity, we confirm the recent prediction [N. Prokof'ev and B.V. Svistunov, Phys. Rev. B 61, 11282 (1999)] that the finite-temperature stiffness parameters ρ^W_x and ρ^W_y determined from the winding number differ from each other and from the true superfluid density ρ_s. Formally, ρ^W_y -> ρ_s in the limit in which L_x -> infinity first and then L_y -> infinity. In practice we find that ρ^W_y converges exponentially to ρ_s for R>1. We also confirm that for 3D systems, ρ^W_x = ρ^W_y = ρ^W_z = ρ_s for any R. In addition, we determine the Kosterlitz-Thouless transition temperature to be T_KT/J=0.34303(8) for the 2D model.

cond-mat.supr-con↗

arXiv2003

Two-Dimensional Quantum XY Model with Ring Exchange and External Field

We present the zero-temperature phase diagram of a square lattice quantum spin 1/2 XY model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the XY-order, striped or valence bond solid, staggered Neel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.

cond-mat.str-el↗

arXiv2001

Magnetic anisotropy of the spin ice compound Dy2Ti2O7

We report magnetization and ac susceptibility of single crystals of the spin ice compound Dy2Ti2O7. Saturated moments at 1.8 K along the charasteristic axes [100] and [110] agree with the expected values for an effective ferromagnetic nearest-neighbor Ising pyrochlore with local <111> anisotropy, where each magnetic moment is constrained to obey the `ice-rule'. At high enough magnetic fields along the [111] axis, the saturated moment exhibits a beaking of the ice-rule; it agrees with the value expected for a three-in one-out spin configuration. Assuming the realistic magnetic interaction between Dy ions given by the dipolar spin ice model, we completely reproduce the results at 2 K by Monte Carlo calculations. However, down to at least 60 mK, we have not found any experimental evidence of the long-range magnetic ordering predicted by this model to occur at around 180 mK. Instead, we confirm the spin freezing of the system below 0.5 K.

cond-mat.str-el↗

arXiv2001

Spin Correlations in Ho$_{2}$Ti$_{2}$O$_{7}$: a Dipolar Spin Ice System

The pyrochlore material $\rm Ho_{2}Ti_{2}O_{7}$ has been suggested to show ``spin ice'' behaviour. We present neutron scattering and specific heat results that establish unambiguously that Ho$_2$Ti$_2$O$_7$ exhibits spin ice correlations at low temperature. Diffuse magnetic neutron scattering from Ho$_2$Ti$_2$O$_7$ is found to be quite well described by a near neighbour spin ice model and very accurately described by a dipolar spin ice model. The heat capacity is well accounted for by the sum of a dipolar spin ice contribution and an expected nuclear spin contribution, known to exist in other Ho$^{3+}$ salts. These results settle the question of the nature of the low temperature spin correlations in $\rm Ho_{2}Ti_{2}O_{7}$ for which contradictory claims have been made.

cond-mat.dis-nn↗

arXiv2000

Studies of the Schroedinger-Newton Equations in D Dimensions

We investigate a $D$ dimensional generalization of the Schroedinger-Newton equations, which purport to describe quantum state reduction as resulting from gravitational effects. For a single particle, the system is a combination of the Schroedinger and Poisson equations modified so that the probability density of the wavefunction is the source of the potential in the Schroedinger equation. For spherically symmetric wavefunctions, a discrete set of energy eigenvalue solutions emerges for dimensions $D<6$, accumulating at D=6. Invoking Heisenberg's uncertainty principle to assign timescales of collapse correspoding to each energy eigenvalue, we find that these timescales may vary by many orders of magnitude depending on dimension. For example, the time taken for the wavefunction of a free neutron in a spherically symmetric state to collapse is many orders of magnitude longer than the age of the universe, whereas for one confined to a box of picometer-sized cross-sectional dimensions the collapse time is about two weeks.

gr-qc↗