arXiv subjects

Erik S. Sorensen

Publications and source records attributed to Erik S. Sorensen.

At least 19 recordsLinked to original sources

arXiv2018

Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain

We study out of time order correlations, $C(x,t)$ and entanglement growth in the random field XX model with open boundary conditions using the exact Jordan-Wigner transformation to a fermionic Hamiltonian. For any non-zero strength of the random field this model describes an Anderson insulator. Two scenarios are considered: A global quench with the initial state corresponding to a product state of the Néel form, and the behaviour in a typical thermal state at $β=1$. As a result of the presence of disorder the information spreading as described by the out of time correlations stops beyond a typical length scale, $ξ_{OTOC}$. For $|x|<ξ_{OTOC}$ information spreading occurs at the maximal velocity $v_{max}=J$ and we confirm predictions for the early time behaviour of $C(x,t)\sim t^{2|x|}$. For the case of the quench starting from the Néel product state we also study the growth of the bipartite entanglement, focusing on the late and infinite time behaviour. The approach to a bounded entanglement is observed to be slow for the disorder strengths we study.

cond-mat.stat-mech↗

arXiv2014

Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography

We compute the non-zero temperature conductivity of conserved flavor currents in conformal field theories (CFTs) in 2+1 spacetime dimensions. At frequencies much greater than the temperature, $\hbarω>> k_B T$, the $ω$ dependence can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large $ω$ results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small $\hbar ω/(k_B T)$. Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large $ω$ behavior for a large class of CFTs. However, for the Wilson-Fisher CFT a relevant "thermal" operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value. We also establish sum rules obeyed by the conductivity of a wide class of CFTs.

cond-mat.str-el↗

arXiv2014

An Exact Diagonalization Study of the Anisotropic Triangular Lattice Heisenberg Model Using Twisted Boundary Conditions

The anisotropic triangular model, which is believed to describe the materials Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper we use twisted boundary conditions and exact diagonalization techniques to study the phase diagram of this model. With these boundary conditions we are able to extract the inter- and intrachain ordering $q$-vectors for the $\frac{J'}{J} < 1$ region finding very close agreement with recent DMRG results on much larger systems. Our results suggest a phase transition between a long-range incommensurate spiral ordered phase, and a more subtle phase with short-range spiral correlations with the $q$-vector describing the incommensurate correlations varying smoothly through the transition. In the latter phase correlations between next-nearest chains exhibits an extremely close competition between predominantly antiferromagnetic and ferromagnetic correlations. Further analysis suggests that the antiferromagnetic next-nearest chain correlations may be slightly stronger than the ferromagnetic ones. This difference is found to be slight but in line with previous renormalization group predictions of a collinear antiferromagnetic ordering in this region.

cond-mat.str-el↗

arXiv2011

Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain

The contribution to the entanglement of an impurity attached to one end of a $J-J_2-delta$ quantum spin chain (S=1/2) is studied. Two different measures of the impurity contribution to the entanglement have been proposed: the impurity-entanglement-entropy S_{imp} and the negativity N. The first, S_{imp}, is based on a subtractive procedure where the entanglement-entropy in the absence of the impurity is subtracted from results with the impurity present. The other, N, is the negativity of a part of the system separated from the impurity and the impurity itself. In this paper we compare the two measures and discuss similarities and differences between them. In the $J-J_2-δ$ model it is possible to perform very precise variational calculations close to the Majumdar-Ghosh-point (J_2 = J / 2 and δ= 0) where the system is gapped with a two-fold degenerate dimerized ground-state. We describe in detail how such calculations are done and how they can be used to calculate N as well as S_{imp} for any impurity-coupling J_K. We then study the complete cross-over in the impurity entanglement as J_K is varied between 0 and 1 close to the Majumdar-Ghosh-point. In particular we study the impurity entanglement when a staggered nearest-neighbour-interaction proportional to $δ$ is introduced. In this case, the two-fold degeneracy of the ground-state is lifted leading to a very rapid reduction in the impurity entanglement as $δ$ is increased.

cond-mat.str-el↗

arXiv2010

Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain

We study the entanglement between two domains of a spin-1 AKLT chain subject to open boundary conditions. In this case the ground-state manifold is four-fold degenerate. We summarize known results and present additional exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the domains and the total system size for {\it all} four degenerate ground-states. In the large $l,L$ limit the entanglement entropy approaches $\ln(2)$ and $2\ln(2)$ for the $S^z_T=\pm 1$ and $S^z_T=0$ states, respectively. In all cases, it is found that this constant is approached exponentially fast defining a length scale $ξ=1/\ln(3)$ equal to the known bulk correlation length.

cond-mat.stat-mech↗

arXiv2009

Entanglement entropy in quantum impurity systems and systems with boundaries

We review research on a number of situations where a quantum impurity or a physical boundary has an interesting effect on entanglement entropy. Our focus is mainly on impurity entanglement as it occurs in one dimensional systems with a single impurity or a boundary, in particular quantum spin models, but generalizations to higher dimensions are also reviewed. Recent advances in the understanding of impurity entanglement as it occurs in the spin-boson and Kondo impurity models are discussed along with the influence of boundaries. Particular attention is paid to 1+1 dimensional models where analytical results can be obtained for the case of conformally invariant boundary conditions and a connection to topological entanglement entropy is made. New results for the entanglement in systems with mixed boundary conditions are presented. Analytical results for the entanglement entropy obtained from Fermi liquid theory are also discussed as well as several different recent definitions of the impurity contribution to the entanglement entropy.

cond-mat.stat-mech↗

arXiv2007

Single-particle Excitation Spectra of C$_{60}$ Molecules and Monolayers

In this paper we present calculations of single-particle excitation spectra of neutral and three-electron-doped Hubbard C$_{60}$ molecules and monolayers from large-scale quantum Monte Carlo simulations and cluster perturbation theory. By a comparison to experimental photoemission, inverse photoemission, and angle-resolved photoemission data, we estimate the intermolecular hopping integrals and the C$_{60}$ molecular orientation angle, finding agreement with recent X-ray photoelectron diffraction (XPD) experiments. Our results demonstrate that a simple effective Hubbard model, with intermediate coupling, $U=4t$, provides a reasonable basis for modeling the properties of C$_{60}$ compounds.

cond-mat.str-el↗

arXiv2006

Boundary effects in the critical scaling of entanglement entropy in 1D systems

We present exact diagonalization and density matrix renormalization group results for the entanglement entropy of critical spin-1/2 XXZ chains. We find that open boundary conditions induce an alternating term in both the energy density and the entanglement entropy which are approximately proportional, decaying away from the boundary with a power-law. The power varies with anisotropy along the XXZ critical line and is corrected by a logarithmic factor, which we calculate analytically, at the isotropic point. A heuristic resonating valence bond explanation is suggested.

cond-mat.str-el↗

arXiv2006

Applications of Cluster Perturbation Theory Using Quantum Monte Carlo Data

We study cluster perturbation theory [Phys. Rev. Lett. \textbf{84}, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard model in one and two dimensions and compare our results for the spectral functions to results obtained using exact diagonalization to solve the cluster hamiltonian. The main advantage of using quantum Monte Carlo results as a starting point is that the initial cluster size can be taken to be considerably larger and hence potentially capture more of the relevant physics. The drawback is that quantum Monte Carlo methods yield results at {\it imaginary} times with stochastic errors.

cond-mat.str-el↗

arXiv2006

Simulations of Disordered Bosons on Hyper-Cubic Lattices

We address computational issues relevant to the study of disordered quantum mechanical systems at very low temperatures. As an example we consider the disordered Bose- Hubbard model in three dimensions directly at the Bose-glass to superfluid phase transition. The universal aspects of the critical behaviour are captured by a (3 + 1) dimensional link-current model for which an efficient 'worm' algorithm is known. We present a calculation of the distribution of the superfluid stiffness over the disorder realizations, outline a number of important considerations for performing such estimates, and suggest a modification of the link-current Hamiltonian that improves the numerical efficiency of the averaging procedure without changing the universal properties of the model.

cond-mat.str-el↗

arXiv2006

Bose-glass to Superfluid transition in the three-dimensional Bose-Hubbard Model

We present a Monte Carlo study of the Bose-glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical (3 + 1) dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as 16x16x16x512 sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent z = 3, in agreement with existing scaling and renormalization group arguments that z = d. We find also a value of $ν= 0.70(12)$ for the correlation length exponent, satisfying the relation $ν>= 2/d$. However, a detailed study of the correlation functions, C(r, tau), at the quantum critical point are not consistent with this value of z. We speculate that this discrepancy could be due to the fact that the correlation functions have not reached their true asymptotic behavior because of the relatively small spatial extent of the lattices used in the present study.

cond-mat.str-el↗

arXiv2004

Imaginary chemical potential quantum Monte Carlo for Hubbard molecules

We generalize the imaginary chemical potential quantum Monte Carlo (QMC) method proposed by Dagotto et al. [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the C$_{60}$ Hubbard molecule are discussed.

cond-mat.str-el↗

arXiv2004

QMC Calculation of the Electronic Binding Energy in a C60 Molecule

Electronic energies are calculated for a Hubbard model on the $C_{60}$ molecule using projector quantum Monte Carlo (QMC). Calculations are performed to accuracy high enough to determine the pair binding energy for two electrons added to neutral $C_{60}$. The method itself is checked against a variety of other quantum Monte Carlo methods as well as exact diagonalization for smaller molecules. The conclusion is that the ground state with two extra electrons on one $C_{60}$ molecule is a triplet and, over the range of parameters where QMC is reliable, has a slightly higher energy than the state with electrons on two separate molecules, so that the pair is unbound.

cond-mat.supr-con↗

arXiv2004

The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.

cond-mat.str-el↗

arXiv2003

Directed geometrical worm algorithm applied to the quantum rotor model

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part,is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore we show how correlation functions, C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and un-directed geometrical worm algorithms. Results for auto-correlation times and Green functions are presented for the quantum rotor model.

cond-mat.str-el↗

arXiv2003

Cluster Monte Carlo Algorithm for the Quantum Rotor Model

We propose a highly efficient "worm" like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the new algorithm even in the presence of disorder. For the pure quantum rotor model with $μ=0$ the new algorithm yields high precision estimates for the critical point $K_c=0.33305(5)$ and the correlation length exponent $ν=0.670(3)$. For the disordered case, $μ=1/2 \pm 1/2$, we find $ν=1.15(10)$.

cond-mat.str-el↗

arXiv2002

Finite Size Scaling of the Spin Stiffness of the Antiferromagnetic S=1/2 XXZ chain

We study the finite size scaling of the spin stiffness for the one-dimensional s=1/2 quantum antiferromagnet as a function of the anisotropy parameter Delta.Previous Bethe ansatz results allow a determination of the stiffness in the thermodynamic limit. The Bethe ansatz equations for finite systems are solvable even in the presence of twisted boundary conditions, a fact we exploit to determine the stiffness exactly for finite systems allowing for a complete determination of the finite size corrections. Relating the stiffness to thermodynamic quantities we calculate the temperature dependence of the susceptibility and its finite size corrections at T=0. A Luttinger liquid approach is used to study the finite size corrections using renormalization group techniques and the results are compared to the numerically exact results obtained using the Bethe ansatz equations. Both irrelevant and marginally irrelevant cases are considered.

cond-mat.str-el↗

arXiv2000

Logrithmic corrections to the RG flow for the two-dimensional bond disordered Ising model

Using the mapping of the partition function of the two-dimensional Ising model onto a pfaffian we evaluate the domain wall free energy difference for the pure and disordered Ising model close to the pure fixed point. Using this method very large lattices can be studied exactly and we confirm that disorder even including frustrating interactions indeed are irrelevant close to the pure fixed point. The finite-size renormalization group flow shows a power-law behavior modified by a logarithmic term that dominates for small lattice sizes.

cond-mat.dis-nn↗