arXiv subjects

A. Honecker

Publications and source records attributed to A. Honecker.

At least 19 recordsLinked to original sources

arXiv2021

Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets

The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.

cond-mat.str-el↗

arXiv2021

Accuracy of the typicality approach using Chebyshev polynomials

Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples.

cond-mat.str-el↗

arXiv2020

A quantum magnetic analogue to the critical point of water

At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs.

cond-mat.str-el↗

arXiv2020

Magnon crystallization in the kagome lattice antiferromagnet

We present numerical evidence for the crystallization of magnons below the saturation field at non-zero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or equivalently flat-band multi-magnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon-crystal is expected to be generic for spin models in dimension $D>1$ where flat-band multi-magnon ground states break translational symmetry.

cond-mat.str-el↗

arXiv2020

Zero-frequency transport properties of one dimensional spin-1/2 systems

We report a detailed analysis of the Drude weights for both thermal and spin transport in one dimensional spin-1/2 systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable XXZ model and second for various non-integrable systems such as the dimerized chain, the frustrated chain, and the spin ladder. We compare our results obtained by exact diagonalization and mean-field theory with the Bethe ansatz, bosonization and other numerical studies in the case of the anisotropic Heisenberg model both in the gapless and gapped regime. In particular, we find indications that the Drude weight for spin transport is finite in the thermodynamic limit for the isotropic chain. For the non-integrable models, a finite-size analysis of the numerical data for the Drude weights is presented covering the entire parameter space of the dimerized and frustrated chain. We also discuss which conclusions can be drawn from bosonization regarding the question whether the Drude weights are finite or not. One of our main results is that the Drude weights vanish in the thermodynamic limit for non-integrable models.

cond-mat.str-el↗

arXiv2016

Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.

cond-mat.str-el↗

arXiv2016

Magnetic excitations in the S = 1/2 antiferromagnetic-ferromagnetic chain compound BaCu2V2O8 at zero and finite temperature

Unlike most quantum systems which rapidly become incoherent as temperature is raised, strong correlations persist at elevated temperatures in $S=1/2$ dimer magnets, as revealed by the unusual asymmetric lineshape of their excitations at finite temperatures. Here we quantitatively explore and parameterize the strongly correlated magnetic excitations at finite temperatures using the high resolution inelastic neutron scattering on the model compound BaCu$_2$V$_2$O$_8$ which we show to be an alternating antiferromagnetic-ferromagnetic spin$-1/2$ chain. Comparison to state of the art computational techniques shows excellent agreement over a wide temperature range. Our findings hence demonstrate the possibility to quantitatively predict coherent behavior at elevated temperatures in quantum magnets.

cond-mat.str-el↗

arXiv2016

Thermodynamic properties of highly frustrated quantum spin ladders: influence of many-particle bound states

Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S=1/2 spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L=200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multi-particle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.

cond-mat.str-el↗

arXiv2016

ESR modes in a Strong-Leg Ladder in the Tomonaga-Luttinger Liquid Phase

Magnetic excitations in the strong-leg quantum spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

cond-mat.str-el↗

arXiv2013

Magnetization of SrCu2(BO3)2 in ultrahigh magnetic fields up to 118 T

The magnetization process of the orthogonal-dimer antiferromagnet SrCu2(BO3)2 is investigated in high magnetic fields of up to 118 T. A 1/2 plateau is clearly observed in the field range 84 to 108 T in addition to 1/8, 1/4 and 1/3 plateaux at lower fields. Using a combination of state-of-the-art numerical simulations, the main features of the high-field magnetization, a 1/2 plateau of width 24 T, a 1/3 plateau of width 34 T, and no 2/5 plateau, are shown to agree quantitatively with the Shastry-Sutherland model if the ratio of inter- to intra-dimer exchange interactions J'/J=0.63. It is further predicted that the intermediate phase between the 1/3 and 1/2 plateau is not uniform but consists of a 1/3 supersolid followed by a 2/5 supersolid and possibly a domain-wall phase, with a reentrance into the 1/3 supersolid above the 1/2 plateau.

cond-mat.str-el↗

arXiv2012

Lanczos algorithm with Matrix Product States for dynamical correlation functions

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex-post reorthogonalization method allows to avoid several shortcomings of the original approach, namely the multi-targeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.

cond-mat.str-el↗

arXiv2012

Location of the Potts-critical end point in the frustrated Ising model on the square lattice

We report on Monte Carlo simulations for the two-dimensional frustrated $J_1$-$J_2$ Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear state different phase-transition scenarios apply depending on the value of the frustration $J_2 / J_1$. In particular a region with critical Ashkin-Teller-like behavior, i.e., a second-order phase transition with varying critical exponents, and a noncritical region with first-order indications were verified. However, the exact transition point $[J_2/J_1]_C$ between both scenarios was under debate. In this paper we present Monte Carlo data which strengthens the conclusion of Jin \et [Phys. Rev. Lett. \textbf{108}, 045702 (2012)] that the transition point is at a value of $J_2/J_1 \approx 0.67$ and that double-peak structures in the energy histograms for larger values of $J_2/J_1$ are unstable in a scaling analysis.

cond-mat.stat-mech↗

arXiv2012

Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the 1D case and develop a numerical algorithm for the 2D case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.

cond-mat.stat-mech↗

arXiv2012

Anisotropic frustrated Heisenberg model on the honeycomb lattice

We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size periodic lattices.

cond-mat.str-el↗

arXiv2012

Multiferroic FeTe$_2$O$_5$Br: Alternating spin chains with frustrated interchain interactions

A combination of density functional theory calculations, many-body model considerations, magnetization and electron spin resonance measurements shows that the multiferroic FeTe$_2$O$_5$Br should be described as a system of alternating antiferromagnetic $S=5/2$ chains with strong Fe-O-Te-O-Fe bridges weakly coupled by two-dimensional frustrated interactions, rather than the previously reported tetramer models. The peculiar temperature dependence of the incommensurate magnetic vector can be explained in terms of interchain exchange striction being responsible for the emergent net electric polarization.

cond-mat.str-el↗

arXiv2011

Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice

Frustration has proved to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model, where only the lowest-energy degrees of freedom are considered. In this paper we study a system corresponding to the strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin 1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J>0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J>0 and J<0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D_6 of the model is present. For J<0, we find a transition temperature T^<_c/|J| = 1.566 +/- 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J>0 the transition occurs at an extremely low temperature, T^>_c ~= 0.0125 J. Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.

cond-mat.str-el↗

arXiv2011

Quantum disordered ground state for hard-core bosons on the frustrated square lattice

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can be represented also by spin-1/2 operators and the model can therefore be mapped onto an anisotropic $J_1$-$J_2$-Heisenberg model. We find the Néel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed for small ferromagnetic exchange terms $J_{1,2}^{x,y}$ and a ferromagnetic phase which orders in the x-y-plane for large $J_{1,2}^{x,y}$. For an intermediate regime the emergence of new quantum states like valence bond crystals or super-solids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing towards a quantum disordered ground state for a small region in the phase diagram.

cond-mat.str-el↗

arXiv2011

Resonances in a dilute gas of magnons and metamagnetism of isotropic frustrated ferromagnetic spin chains

We show that spin-S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.

cond-mat.str-el↗