arXiv subjects

Erik Sorensen

Publications and source records attributed to Erik Sorensen.

13 recordsLinked to original sources

arXiv2018

Estimates of the Quantum Fisher Information in the $S=1$ Anti-Ferromagnetic Heisenberg Spin Chain with Uniaxial Anisotropy

The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite entanglement is present. Recent results have related the quantum Fisher information to experimentally measurable probes. While in principle possible, a direct evaluation of the quantum Fisher information at finite temperatures is technically challenging and here we show that a simple estimate can be obtained for materials where the single mode approximation is valid. We focus on the $S=1$ anti-ferromagnetic Heisenberg model with uniaxial anisotropy. Quantum Monte Carlo thechniques are used to determine low temperature correlations from which the quantum Fisher information can be estimated within the single mode approximation. The quantum Fisher information is compared to the quantum variance for the staggered magnetization operators in the transverse direction and inequalities between the quantum Fisher information, the quantum variance and the full variance are discussed. Both the quantum and full variance as well as the quantum Fisher information are examined at finite temperatures above the isotropic point and at the quantum critical point for the Haldane-Néel transtion. A finite size scaling study of the quantum Fisher information is performed at the quantum critical point and used to confirm the Ising nature of the Haldane-Néel transition.

cond-mat.str-el↗

arXiv2013

The dynamics of quantum criticality via Quantum Monte Carlo and holography

Understanding the real time dynamics of quantum systems without quasiparticles constitutes an important yet challenging problem. We study the superfluid-insulator quantum-critical point of bosons on a two-dimensional lattice, a system whose excitations cannot be described in a quasiparticle basis. We present detailed quantum Monte Carlo results for two separate lattice realizations: their low-frequency conductivities are found to have the same universal dependence on imaginary frequency and temperature. We then use the structure of the real time dynamics of conformal field theories described by the holographic gauge/gravity duality to make progress on the difficult problem of analytically continuing the Monte Carlo data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point, and on the spectrum of quasinormal modes in the vicinity of the superfluid-insulator quantum phase transition. Extensions to other observables and universality classes are discussed.

cond-mat.str-el↗

arXiv2013

Exact Real Time Dynamics of Quantum Spin Systems Using the Positive-P Representation

We discuss a scheme for simulating the real time quantum quench dynamics of interacting quantum spin systems within the positive-P formalism. As model systems we study the transverse field Ising model as well as the Heisenberg model undergoing a quench away from the classical ferromagnetic ordered state and antiferromagnetic Neel state, depending on the sign of the Heisenberg exchange interaction. The connection to the positive-P formalism as it is used in quantum optics is established by mapping the spin operators on to Schwinger bosons. In doing so, the dynamics of the interacting quantum spin system is mapped onto a set of Ito stochastic differential equations (SDEs) the number of which scales linearly with the number of spins, N, compared to an exact solution through diagonalization that in the case of the Heisenberg model would require matrices exponentially large in N . This mapping is exact and can be extended to higher dimensional interacting systems as well as to systems with an explicit coupling to the environment.

cond-mat.stat-mech↗

arXiv2013

Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques

We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation is superior in practice to an earlier phase space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times several fold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse field Ising model in one and two dimensions

cond-mat.stat-mech↗

arXiv2013

Scaling of entanglement entropy across Lifshitz transitions

We investigate the scaling of the bipartite entanglement entropy across Lifshitz quantum phase transitions, where the topology of the Fermi surface changes without any changes in symmetry. We present both numerical and analytical results which show that Lifshitz transitions are characterized by a well-defined set of critical exponents for the entanglement entropy near the phase transition. In one dimension, we show that the entanglement entropy exhibits a length scale that diverges as the system approaches a Lifshitz critical point. In two dimensions, the leading and sub-leading coefficients of the scaling of entanglement entropy show distinct power-law singularities at critical points. The effect of weak interactions is investigated using the density matrix renormalization group algorithm.

cond-mat.str-el↗

arXiv2011

General Quantum Fidelity Susceptibilities for the J1-J2 Chain

We study slightly generalized quantum fidelity susceptibilities where the differential change in the fidelity is measured with respect to a different term than the one used for driving the system towards a quantum phase transition. As a model system we use the spin-1/2 J1-J2 antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, chi_p, chi_D and chi_AF, which are related to the spin stiffness, the dimer order and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the J1-J2 model. We show that they all can accurately identify a quantum critical point in this model occurring at J2 = 0.241J1 between a gapless Heisenberg phase for J2 < J2_critical and a dimerized phase for J2 > J2_critical. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.

cond-mat.str-el↗

arXiv2005

Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from w_k-scaling of the conductivity towards w_k/T-scaling at low Matsubara frequencies w_k. By careful analytic continuation using Pade approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with w/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be 0.45(5)Q^2/h, distinct from previous estimates in the T=0, w/T >> 1 limit.

cond-mat.other↗

arXiv1998

Non-trivial fixed point structure of the two-dimensional +-J 3-state Potts ferromagnet/spin glass

The fixed point structure of the 2D 3-state random-bond Potts model with a bimodal ($\pm$J) distribution of couplings is for the first time fully determined using numerical renormalization group techniques. Apart from the pure and T=0 critical fixed points, two other non-trivial fixed points are found. One is the critical fixed point for the random-bond, but unfrustrated, ferromagnet. The other is a bicritical fixed point analogous to the bicritical Nishimori fixed point found in the random-bond frustrated Ising model. Estimates of the associated critical exponents are given for the various fixed points of the random-bond Potts model.

cond-mat.dis-nn↗

arXiv1996

Integer Quantum Hall Effect in Double-Layer Systems

We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models and on transfer matrix calculations for phenomenological network models. The microscopic calculations indicate a crossover regime for weak interlayer tunneling in which the correlation length exponent appears to increase. Comparison of network model calculations with microscopic calculations casts doubt on their generic applicability.

cond-mat↗

arXiv1995

Scaling theory of the Kondo screening cloud

A scaling form for the local susceptibility, derived from renormalization group arguments, is proposed. The scale over which the uniform part of this scaling form varies can be viewed as a definition of the Kondo ``screening cloud" $\sim ξ_K$. The proposed scaling form interpolates between Ruderman-Kittel-Kasuya-Yosida (RKKY) results in the high temperature limit, $T\gg T_K$, and Fermi liquid results in the low temperature, long-distance limit, $T\ll T_K$, $r\gg ξ_K$. The predicted form of the Knight shift is longer range at low temperatures where the screening cloud has formed, than at high temperatures where it has not. Using weak and strong coupling perturbation theory combined with large scale density matrix renormalization group (DMRG) results we study the validity of the finite size version of the scaling form at $T=0$. We explicitly extract a length scale proportional to the Kondo length scale, $ξ_K$. The numerical results are in good agreement with the proposed scaling form and confirm the existence of the Kondo screening cloud.

cond-mat↗

arXiv1995

First Order Superconductor to Insulator Transition: Evidence for a Supersolid Phase

The superconductor to insulator transition in the presence of long-range Coulomb interactions is studied using Monte Carlo techniques. At integer filling the transition is second order. At half filling we find evidence of a first order transition to a state with non-zero $S_{π,π}$. No intervening supersolid phase is observed. Off half-filling two separate transitions are found. The transition from the superconducting to a supersolid phase is second order followed by another second order transition between the supersolid and an insulating phase.

cond-mat↗

arXiv1995

Is there an exponentially large Kondo screening cloud ?

We make a precise scaling conjecture, based on renormalization group ideas, regarding the screening cloud around an impurity spin in the Kondo effect and test it numerically using the Density Matrix Renormalization Group method.

cond-mat↗

arXiv1994

Impurities in $s=1$ Heisenberg Antiferromagnets

The $s=1$ Heisenberg Antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with $J'\ne J$ at the center of an even-length open chain is considered. Using the density matrix renormalization group method we find that, for sufficiently strong or weak $J'$, a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on $s=1/2$ chain-end excitations, both in the weak and strong coupling limit. In a region around the uniform limit, $J'=J$, no states are found with energy below the Haldane gap. Secondly, a $s=1/2$ impurity at the center of an otherwise even-length open chain is considered. The coupling to the $s=1/2$ impurity is varied. Bound states in the Haldane gap are found {\it only} for sufficiently weak (antiferromagnetic) coupling. For a $s=1/2$ impurity coupled with a strong (antiferromagnetic) bond, {\it no} states are found in the Haldane. Our results are in good qualitative agreement with recent experiments on doped NENP and Y$_2$BaNiO$_5$.

cond-mat↗