arXiv subjects

Andreas M. Läuchli

Publications and source records attributed to Andreas M. Läuchli.

At least 73 records · Page 4Linked to original sources

arXiv2013

Entanglement negativity via replica trick: a Quantum Monte Carlo approach

Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. These quantities can serve as witnesses of criticality. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. These are more pronounced in the presence of boundaries. For large chains we find perfect agreement with CFT. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. Remarkably, the finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.

cond-mat.str-el↗

arXiv2013

Numerical study of magnetization plateaux in the spin-1/2 kagome Heisenberg antiferromagnet

We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.

cond-mat.str-el↗

arXiv2013

Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope

We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi-Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.

cond-mat.quant-gas↗

arXiv2013

Entanglement Spectroscopy using Quantum Monte Carlo

We present a numerical scheme to reconstruct a subset of the entanglement spectrum of quantum many body systems using quantum Monte Carlo. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasi-degeneracy of the entanglement spectrum in the Haldane-Insulator phase. In general the method is able to reconstruct the largest few eigenvalues in each symmetry sector and typically performs better when the eigenvalues are not too different.

cond-mat.quant-gas↗

arXiv2013

An entropy perspective on the thermal crossover in a fermionic Hubbard chain

We study the Renyi entropy in the finite temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground state entropy has characteristic features such as a logarithmic divergence with block size and $2\kF$ oscillations that are a hallmark of its Luttinger liquid nature. The interplay between the (extensive) thermal entropy and the ground state features is studied and we analyze the temperature induced decay of the amplitude of the oscillations as well as the scaling of the purity. Furthermore, we show how the spin and charge velocities can be extracted from the temperature dependence of the Renyi entropy, bridging our findings to recent experimental proposals on how to implement the measurement of Renyi entropies in cold atom system. Studying the Renyi mutual information, we also demonstrate how constraints such as particle number conservation can induce persistent correlations visible in the mutual information even at high temperature.

cond-mat.str-el↗

arXiv2013

Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance

To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.

cond-mat.str-el↗

arXiv2013

Operator content of real-space entanglement spectra at conformal critical points

We provide numerical evidence that the low-lying part of the entanglement spectrum of a real-space block (i.e. a single interval) of a one-dimensional quantum many body system at a conformal critical point corresponds to the energy spectrum of a boundary conformal field theory (CFT). This correspondence allows to uncover a subset of the operator content of a conformal field theory by inspection of the entanglement spectrum of a single wave function, thus providing important information on a CFT beyond its central charge. As a practical application we show that for many systems described by a compactified boson CFT, one can infer the compactification radius (governing e.g. the power law decay of correlation functions) of the theory in a simple way based on the entanglement spectrum.

cond-mat.stat-mech↗

arXiv2013

Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state

Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension $D$. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small $D$ the dimer state has a lower variational energy than the plaquette state, however, for large $D$ it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are non-chiral flux states.

cond-mat.str-el↗

arXiv2012

Realizing Fractional Chern Insulators with Dipolar Spins

Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the ν=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications.

cond-mat.str-el↗

arXiv2012

Entanglement Spectra of Heisenberg Ladders of higher Spin

We study the entanglement spectrum of Heisenberg spin ladders of arbitrary spin length S in the perturbative regime of strong rung coupling. For isotropic spin coupling the the entanglement spectrum is, within first order perturbation theory, always proportional to the energy spectrum of the single chain with a proportionality factor being also independent of S. A more complicated situation arises for anisotropic ladders of higher spin S>=1 since here even the unperturbed ground state has a nontrivial entanglement spectrum. Finally we discuss related issues in dimerized spin chains.

cond-mat.stat-mech↗

arXiv2012

Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions

We consider the von Neumann and Rényi entropies of the one dimensional quarter-filled Hubbard model. We observe that for periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We explain this observation in terms of a shell-filling effect, and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems.

cond-mat.str-el↗

arXiv2012

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS). For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [PRL 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m=0.2-0.4 in the thermodynamic limit.

cond-mat.str-el↗

arXiv2012

Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry

We study the entanglement spectrum of spin-1/2 XXZ ladders both analytically and numerically. Our analytical approach is based on perturbation theory starting either from the limit of strong rung coupling, or from the opposite case of dominant coupling along the legs. In the former case we find to leading order that the entanglement Hamiltonian is also of nearest-neighbor XXZ form although with an in general renormalized anisotropy. For the cases of XX and isotropic Heisenberg ladders no such renormalization takes place. In the Heisenberg case the second order correction to the entanglement Hamiltonian consists of a renormalization of the nearest neighbor coupling plus an unfrustrated next nearest neighbor coupling. In the opposite regime of strong coupling along the legs, we point out an interesting connection of the entanglement spectrum to the Lehmann representation of single chain spectral functions of operators appearing in the physical Hamiltonian coupling the two chains.

cond-mat.str-el↗

arXiv2011

Multi-orbital Kondo physics of Co in Cu hosts

We investigate the electronic structure of cobalt atoms on a copper surface and in a copper host by combining density functional calculations with a numerically exact continuous-time quantum Monte Carlo treatment of the five-orbital impurity problem. In both cases we find low energy resonances in the density of states of all five Co $d$-orbitals. The corresponding self-energies indicate the formation of a Fermi liquid state at low temperatures. Our calculations yield the characteristic energy scale -- the Kondo temperature -- for both systems in good agreement with experiments. We quantify the charge fluctuations in both geometries and suggest that Co in Cu must be described by an Anderson impurity model rather than by a model assuming frozen impurity valency at low energies. We show that fluctuations of the orbital degrees of freedom are crucial for explaining the Kondo temperatures obtained in our calculations and measured in experiments.

cond-mat.str-el↗

arXiv2011

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field

We investigate the properties of the Heisenberg S=1 chain with bilinear and biquadratic interactions in a magnetic field using the Density Matrix Renormalization Group, Bethe ansatz and field theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This liquid undergoes a continuous pair unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector chiral phase.

cond-mat.str-el↗

arXiv2011

Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice

We perform large scale finite-temperature Monte Carlo simulations of the classical $e_g$ and $t_{2g}$ orbital models on the simple cubic lattice in three dimensions. The $e_g$ model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent $ν\approx0.66(1)$ is close to the 3D XY value, the exponent $η\approx 0.15(1)$ differs substantially from O(N) values. At $T_c$ a U(1) symmetry emerges, which persists for $T<T_c$ below a crossover length scaling as $Λ\sim ξ^a$, with an unusually small $a\approx1.3$. Finally, for the $t_{2g}$ model we find a {\em first order} transition into a low-temperature lattice-nematic phase without orbital order.

cond-mat.str-el↗

arXiv2011

Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C5H12N)2CuBr4 (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.

cond-mat.str-el↗

arXiv2010

Bridging frustrated-spin-chain and spin-ladder physics: quasi-one-dimensional magnetism of BiCu2PO6

We derive and investigate the microscopic model of the quantum magnet BiCu2PO6 using band structure calculations, magnetic susceptibility and high-field magnetization measurements, as well as ED and DMRG techniques. The resulting quasi-one-dimensional spin model is a two-leg AFM ladder with frustrating next-nearest-neighbor couplings along the legs. The individual couplings are estimated from band structure calculations and by fitting the magnetic susceptibility with theoretical predictions, obtained using ED. The nearest-neighbor leg coupling J1, the rung coupling J4, and one of the next-nearest-neighbor couplings J2 amount to 120-150 K, while the second next-nearest-neighbor coupling is J2'~J2/2. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions J2 and J2' have very similar superexchange pathways, they differ substantially in magnitude due to a tiny difference in the O-O distances and in the arrangement of non-magnetic PO4 tetrahedra. An extensive ED study of the proposed model provides the low-energy excitation spectrum and shows that the system is in the strong rung coupling regime. The strong frustration by the next-nearest-neighbor couplings leads to a triplon branch with an incommensurate minimum. This is further corroborated by a strong-coupling expansion up to second order in the inter-rung coupling. Based on high-field magnetization measurements, we estimate the spin gap of 32 K and suggest the likely presence of antisymmetric DM anisotropy and inter-ladder coupling J3. We also provide a tentative description of the physics of BiCu2PO6 in magnetic field, in the light of the low-energy excitation spectra and numerical calculations based on ED and DMRG. In particular, we raise the possibility for a rich interplay between one- and two-component Luttinger liquid phases and a magnetization plateau at 1/2 of the saturation value.

cond-mat.mtrl-sci↗