arXiv subjects

Stefan Wessel

Publications and source records attributed to Stefan Wessel.

At least 55 records · Page 3Linked to original sources

arXiv2018

The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C$_9$H$_{18}$N$_2$CuBr$_4$

Polarized inelastic neutron scattering experiments recently identified the amplitude (Higgs) mode in C$_9$H$_{18}$N$_2$CuBr$_4$, a two-dimensional near-quantum-critical spin-1/2 two-leg ladder compound, which exhibits a weak easy-axis exchange anisotropy. Here, we theoretically examine the dynamic spin structure factor of such planar coupled spin-ladder systems using large-scale quantum Monte Carlo simulations. This allows us to provide a quantitative account of the experimental neutron scattering data within a consistent quantum spin model. Moreover, we trance the details of the continuous evolution of the amplitude mode from a two-particle bound state of coupled ladders in the classical Ising limit all the way to the quantum spin-1/2 Heisenberg limit with fully restored SU(2) symmetry, where it gets overdamped by the two-magnon continuum in neutron scattering.

cond-mat.str-el↗

arXiv2018

Spin dynamics of coupled spin ladders near quantum criticality in Ba2CuTeO6

We report inelastic neutron scattering measurements of the magnetic excitations in Ba2CuTeO6, proposed by ab initio calculations to magnetically realize weakly coupled antiferromagnetic two-leg spin-1/2 ladders. Isolated ladders are expected to have a singlet ground state protected by a spin gap. Ba2CuTeO6 orders magnetically, but with a small Neel temperature relative to the exchange strength, suggesting that the interladder couplings are relatively small and only just able to stabilize magnetic order, placing Ba2CuTeO6 close in parameter space to the critical point separating the gapped phase and Neel order. Through comparison of the observed spin dynamics with linear spin wave theory and quantum Monte Carlo calculations, we propose values for all relevant intra- and interladder exchange parameters, which place the system on the ordered side of the phase diagram in proximity to the critical point. We also compare high field magnetization data with quantum Monte Carlo predictions for the proposed model of coupled ladders.

cond-mat.str-el↗

arXiv2018

Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice

The antiferromagnetic Ising model on the pyrochlore lattice exhibits a quantum phase transition in an applied transverse field from the low-field quantum spin-ice phase to the high-field polarized regime. Recent field-theoretical analysis and series expansion results indicate this to be a discontinuous, first-order transition. Here, we explore this transition using quantum Monte Carlo simulations in order to assess this scenario and study the thermodynamic properties in the vicinity of the quantum phase transition. For this purpose, we also consider several variants of extended cluster-update schemes for the transverse field Ising antiferromagnet on frustrated lattices and compare their performance to the conventional bond-based algorithm for the transverse field Ising model on the pyrochlore lattice.

cond-mat.str-el↗

arXiv2018

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S=1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter- and intradimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding "sign-problem-free" model, obtained by changing the signs of all positive off-diagonal matrix elements in the dimer basis. By exploiting this insight, we map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to zero temperature. For larger coupling ratios, our QMC results assist us in benchmarking the evolution of the thermodynamic properties by systematic comparison with exact diagonalization calculations and interpolated high-temperature series expansions.

cond-mat.str-el↗

arXiv2018

Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet

We consider the finite-temperature phase diagram of the $S = 1/2$ frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer and the dimer-singlet state terminates on the first-order line, giving a quantum critical end point, and we use tensor-network calculations to follow the first-order discontinuities in its vicinity.

cond-mat.str-el↗

arXiv2018

Diagnosing Fractionalization from the Spin Dynamics of $Z_2$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations

Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice quantum spin-$1/2$ model, which is known to harbor an extended $Z_2$ quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit-cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the $Z_2$ quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.

cond-mat.str-el↗

arXiv2018

Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.

cond-mat.str-el↗

arXiv2018

Parameter diagnostics of phases and phase transition learning by neural networks

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.

cond-mat.stat-mech↗

arXiv2018

Pairing and chiral spin density wave instabilities on the honeycomb lattice: a comparative quantum Monte Carlo study

Using finite-temperature determinantal quantum Monte Carlo calculations, we re-examine the pairing susceptibilities in the Hubbard model on the honeycomb lattice, focusing on doping levels onto and away from the van Hove singularity (VHS) filling. For this purpose, electronic densities of $0.75$ (at the hole-doping VHS) and $0.4$ (well below the VHS) are considered in detail, where due to a severe sign problem at strong coupling strengths, we focus on the weak interaction region of the Hubbard model Hamiltonian. From analyzing the temperature dependence of pairing susceptibilities in various symmetry channels, we find the singlet $d$+$id$-wave to be the dominant pairing channel both at and away from the VHS filling. We furthermore investigate the electronic susceptibility to a specific chiral spin density wave (SDW) order, which we find to be similarly relevant at the VHS, while it extenuates upon doping away from the VHS filling.

cond-mat.str-el↗

arXiv2017

Finite-Temperature Dynamics and Thermal Intraband Magnon Scattering in Haldane Spin-One Chains

The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations and quantum Monte Carlo simulations. Open finite chains exhibit a sub-gap band in the thermal spectral functions, indicative of localized edge-states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the Haldane spin-one chain is shown to result from intra-band magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio. These findings are discussed with respect to possible future studies on spin-one chain compounds based on inelastic neutron scattering.

cond-mat.str-el↗

arXiv2017

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.

cond-mat.mes-hall↗

arXiv2017

Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder

Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L=200 rungs (400 spins 1/2) and down to very low temperatures.

cond-mat.str-el↗

arXiv2017

Critical behavior in the presence of an order-parameter pinning field

We apply a recently advocated simulation scheme that employs a local order-parameter pinning field to study quantum critical phenomena in the two-dimensional square-lattice bilayer quantum Heisenberg model. Using a world-line quantum Monte Carlo approach, we show that for this model, the pinning-field approach allows to locate the quantum critical point over a wide range of pinning-field strengths. However, the identification of the quantum critical scaling behavior is found to be hard since the pinning field introduces strong corrections to scaling. In order to further elucidate the scaling behavior in this situation, we also study an improved classical lattice model in the three-dimensional Ising universality class by means of Monte Carlo simulations on large lattice sizes, which allow us to employ refined finite-size scaling considerations. A renormalization group analysis exhibits the presence of an important crossover effect from the zero pinning-field to a critical adsorption fixed point. In line with field-theoretical results, we find that at the critical adsorption fixed point the short-distance expansion of the order-parameter profile exhibits a new universal critical exponent. This result also implies the presence of slowly decaying scaling corrections, which we analyze in detail.

cond-mat.stat-mech↗

arXiv2016

Excitation Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

By means of large-scale quantum Monte Carlo simulations, we examine the quantum critical scaling of the magnetic excitation gap (the triplon gap) in a three-dimensional dimerized quantum antiferromagnet, the bicubic lattice, and identify characteristic multiplicative logarithmic scaling corrections atop the leading mean-field behavior. These findings are in accord with field-theoretical predictions that are based on an effective description of the quantum critical system in terms of an asymptotically-free field theory, which exhibits a logarithmic decay of the renormalized interaction strength upon approaching the quantum critical point. Furthermore, using bond-based singlet spectroscopy, we identify the amplitude (Higgs) mode resonance within the antiferromagnetic region. We find a Higgs mass scaling in accord with field-theoretical predictions that relate it by a factor of $\sqrt{2}$ to the corresponding triplon gap in the quantum disordered regime. In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. The width of the Higgs mode resonance is observed to scale linearly with the Higgs mass near criticality, indicative of this critically well-defined excitation mode of the symmetry broken phase.

cond-mat.str-el↗

arXiv2016

Competing pairing channels in the doped honeycomb lattice Hubbard model

Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet to $p+ip$ triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) and are performed using DCA simulations with an interaction-expansion continuous-time quantum Monte Carlo cluster solver. We calculated explicitly the temperature dependence of different uniform superconducting pairing susceptibilities and found a consistent picture emerging upon gradually increasing the cluster size: while at weak coupling the $d+id$ singlet pairing dominates close to the VHS filling, an enhanced tendency towards $p$-wave triplet pairing upon further increasing the interaction strength is observed. The relevance of these systematic results for existing proposals and ongoing pursuits of odd-parity topological superconductivity are also discussed.

cond-mat.str-el↗

arXiv2016

Thermal Ising transitions in the vicinity of two-dimensional quantum critical points

The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the ${\it chiral}$ Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case we extract values of the critical exponents $ν$ and $η$, related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground state quantum Monte Carlo calculations as well as analytical approaches.

cond-mat.str-el↗

arXiv2015

Correlations and entanglement in quantum critical bilayer and necklace XY models

We analyze the critical properties and the entanglement scaling at the quantum critical points of the spin-half XY model on the two-dimensional square-lattice bilayer and necklace lattice, based on quantum Monte Carlo simulations on finite tori and for different subregion shapes. For both models, the finite-size scaling of the transverse staggered spin structure factor is found in accord with a quantum critical point described by the two-component, three-dimensional $ϕ^4$-theory. The second Rényi entanglement entropy in the absence of corners along the subsystem boundary exhibits area-law scaling in both models, with an area-law prefactor of $0.0674(7)$ [$0.0664(4)$] for the bilayer [necklace] model, respectively. Furthermore, the presence of $90^{\circ}$ corners leads to an additive logarithmic term in both models. We estimate a contribution of $-0.010(2)$ [$-0.009(2)$] due to each $90^{\circ}$ corner to the logarithmic correction for the bilayer [necklace] model, and compare our findings to recent numerical linked cluster calculations and series expansion results on related models.

cond-mat.str-el↗

arXiv2015

Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice

We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal density-density interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strong-coupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism.

cond-mat.str-el↗