arXiv subjects

R. Moessner

Publications and source records attributed to R. Moessner.

At least 73 records · Page 4Linked to original sources

arXiv2014

Finite-size scaling of eigenstate thermalization

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite, and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic non-integrable systems these fluctuations scale with a universal power law $D^{-1/2}$ with the dimension $D$ of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models, and several observables for each model. Each family includes integrable members, and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

cond-mat.stat-mech↗

arXiv2013

Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets

We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks.

cond-mat.str-el↗

arXiv2013

Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes

Topological states of matter present a wide variety of striking new phenomena. Prominent among these is the fractionalisation of electrons into unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or magnetic monopoles [3]. Their detection, however, is fundamentally complicated by the lack of any local order, such as, for example, the magnetisation in a ferromagnet. While there are now several instances of candidate topological spin liquids [4], their identification remains challenging [5]. Here, we provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases. We show that there are direct signatures - qualitative and quantitative - of the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. These include counterintuitive manifestations of quantum number fractionalisation, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalisation of electron spin. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches.

cond-mat.str-el↗

arXiv2013

Correlations and phase structure of Ising models at complex temperature

We investigate the spin-spin correlation functions of Ising magnets at complex values of the temperature, T. For one-dimensional chain and ladder systems, we show the existence of a kind of helimagnetic order in the vicinity of contours where the leading two eigenvalues of the transfer matrix become equal in magnitude. We analyse the development of long-range order as the two-dimensional limit is approached, and find that there is rich structure in much of the complex-T plane. In particular, and contrary to the work of Fisher on this problem, the development of long-range order is actually associated with a proliferation of partition function zeros in a certain finite region of that plane containing the real-temperature magnetically ordered phase. The thermodynamic consequences of this are also discussed.

cond-mat.str-el↗

arXiv2013

Approximating random quantum optimization problems

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution space over `classical' product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are: (i) The derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment. (ii) A demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects structure of the solution space of random $k$-QSAT. Simulated annealing exhibits metastability in similar `hard' regions of parameter space. (iii) A generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy `landscape' of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$-QSAT in a two-dimensional energy-density--clause-density space.

cond-mat.stat-mech↗

arXiv2013

Coulomb phase diagnostics as function of temperature, interaction range and disorder

The emergent gauge field characteristic of the Coulomb phase of spin ice betrays its existence via pinch points in the spin structure factor ${\cal{S}}$ in reciprocal space which takes the form of a transverse projector ${\cal{P}}$ at low temperature: ${\cal{S}} (q) \sim {\cal{P}} \sim q^2_\bot/q^2$. We develop a theory which establishes the fate of the pinch points at low and high temperature, for hard and soft spins, for short- and long-ranged (dipolar) interactions, as well as in the presence of disorder. We find that their detailed shape can be used to read off the relative sizes of entropic and magnetic Coulomb interactions of monopoles in spin ice, and we resolve the question why pinch points have been experimentally observed for Ho$_{1.7}$Y$_{0.3}$Ti$_2$O$_7$ even at high temperature in the presence of strong disorder.

cond-mat.str-el↗

arXiv2013

Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice

Ever since the experiments which founded the field of highly frustrated magnetism, the kagome Heisenberg antiferromagnet has been the archetypical setting for the study of fluctuation induced exotic ordering. To this day the nature of its classical low-temperature state has remained a mystery: the non-linear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature. Here we present an efficient Monte Carlo algorithm which removes the latter obstacle. Our simulations detect a low-temperature regime in which correlations saturate at a remarkably small value. Feeding these results into an effective model and analyzing the results in the framework of an appropriate field theory implies the presence of long-range dipolar spin order with a tripled unit cell.

cond-mat.str-el↗

arXiv2012

Disorder by disorder and flat bands in the kagome transverse field Ising model

We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second-order quantum phase transition in the 3d XY universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields h. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order eight in the 1/h limit. This behaviour can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion.

cond-mat.str-el↗

arXiv2012

High temperature onset of field-induced transitions in the spin-ice compound Dy2Ti2O7

We have studied the field-dependent ac magnetic susceptibility of single crystals of Dy2Ti2O7 spin ice along the [111] direction in the temperature range 1.8 K - 7 K. Our data reflect the onset of local spin ice order in the appearance of different field regimes. In particular, we observe a prominent feature at approximately 1.0 T that is a precursor of the low-temperature metamagnetic transition out of field-induced kagome ice, below which the kinetic constraints imposed by the ice rules manifest themselves in a substantial frequency-dependence of the susceptibility. Despite the relatively high temperatures, our results are consistent with a monopole picture, and they demonstrate that such a picture can give physical insight to the spin ice systems even outside the low-temperature, low-density limit where monopole excitations are well-defined quasiparticles.

cond-mat.str-el↗

arXiv2012

Incommensurate magnetic fluctuations and Fermi surface topology in LiFeAs

Using the angle-resolved photoemission spectroscopy (ARPES) data accumulated over the whole Brillouin zone (BZ) in LiFeAs we analyze the itinerant component of the dynamic spin susceptibility in this system in the normal and superconducting state. We identify the origin of the incommensurate magnetic inelastic neutron scattering (INS) intensity as scattering between the electron pockets, centered around the $(π,π)$ point of the BZ and the large two-dimensional hole pocket, centered around the $Γ$-point of the BZ. As the magnitude of the superconducting gap within the large hole pocket is relatively small and angle dependent, we interpret the INS data in the superconducting state as a renormalization of the particle-hole continuum rather than a true spin exciton. Our comparison indicates that the INS data can be reasonably well described by both the sign changing symmetry of the superconducting gap between electron and hole pockets as well as sign preserving gap, depending on the assumptions made for the fermionic damping.

cond-mat.supr-con↗

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

Designing Topological Bands in Reciprocal Space

Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically non-trivial band structures. Our approach is simple and direct: it amounts to considering tight-binding models directly in reciprocal space. These models naturally cause atoms to experience highly uniform magnetic flux density and lead to topological bands with very narrow dispersion, without fine-tuning of parameters. Further, our construction immediately yields instances of optical Chern lattices, as well as band structures of higher Chern number, |C|>1.

cond-mat.quant-gas↗

arXiv2012

A Bionic Coulomb Phase on the Pyrochlore Lattice

A class of three dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit "Coulomb" phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a new example of this phenomenon-the four state Potts model on the pyrochlore lattice-where the long wavelength description now involves three independent gauge fields as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops shows a scaling with loop length and system size previously identified as characteristic of Coulomb phases.

cond-mat.stat-mech↗

arXiv2012

Switching the Anomalous DC Response of an AC-driven Quantum Many-body system

For a class of integrable quantum many-body systems, symmetric AC driving can generically produce a steady DC response. We show how such dynamical freezing can be switched off, not by forcing the system to follow the (arbitrarily fast) driving field, but rather through a much slower but complete oscillation of each individual mode of the system at a frequency of its own, with the slowest mode exhibiting a divergent period. This switching can be controlled in detail, its sharpness depending on a particular parameter of the Hamiltonian. The phenomenon has a robust manifestation even in the few-body limit, perhaps the most promising setting for realisation within existing frameworks.

cond-mat.stat-mech↗

arXiv2012

Hierarchy of fractional Chern insulators and competing compressible states

We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling. We find hierarchy multiplets of incompressible states at fillings ν=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as ν=1/5,2/7. These are accounted for by an analogy to Haldane pseudopotentials extracted from an analysis of the two-particle problem. Important distinctions to standard fractional quantum Hall physics are striking: absent particle-hole symmetry in a single band, an interaction-induced single-hole dispersion appears, which perturbs and eventually destabilizes incompressible states as νincreases. For this reason the nature of the state at ν=2/3 is hard to pin down, while ν=5/7,4/5 do not seem to be incompressible in our system.

cond-mat.str-el↗

arXiv2012

A field trip through spin ice

Fractionalisation -- the breaking up of an apparently indivisible microscopic degree of freedom -- is one of the most counterintuitive phenomena in many-body physics. Here we study its most fundamental manifestation in spin ice, the only known fractionalised magnetic compound in 3D: we directly visualise the $1/r^2$ magnetic Coulomb field of monopoles which emerge as the atomic magnetic dipoles fractionalise. We analyse the internal magnetic field distribution, relevant for local experimental probes. In particular, we present new zero-field NMR measurements which exhibit excellent agreement with the calculated lineshapes, noting that this experimental technique can in principle measure directly the monopole density in spin ice. The distribution of field strengths is captured by a simple analytical form which exhibits a low density of low-field sites---in apparent disagreement with reported $μ$SR results. Counterintuitively, the density of low-field locations decreases as the local ferromagnetic correlations imposed by the ice rules weaken.

cond-mat.str-el↗

arXiv2012

Multicomponent Skyrmion lattices and their excitations

We study quantum Hall ferromagnets with a finite density topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a $d$-component complex spinor field. In the absence of anisotropies, we find formation of a hexagonal Skyrmion lattice which completely breaks the underlying SU(d) symmetry. The ground state charge density modulation, which inevitably exists in these lattices, vanishes exponentially in $d$. We compute analytically the complete low-lying excitation spectrum, which separates into $d^{2}-1$ gapless acoustic magnetic modes and a magnetophonon. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant for experiments with AlAs quantum wells. Here, we find a transition, which breaks a six-fold rotational symmetry of a triangular lattice, followed by a formation of a square lattice at large values of anisotropy strength.

cond-mat.str-el↗

arXiv2012

Quantum order by disorder and accidental soft mode Er2Ti2O7

Motivated by recent neutron scattering experiments, we derive and study an effective "pseudo-dipolar" spin-1/2 model for the XY pyrochlore antiferromagnet Er2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it does lead to a one-parameter `accidental' classical degeneracy. This degeneracy is lifted by quantum fluctuations in favor of the non-coplanar spin structure observed experimentally -- a rare experimental instance of quantum order by disorder. A non-Goldstone low-energy mode is present in the excitation spectrum in accordance with inelastic neutron scattering data. Our theory also resolves the puzzle of the experimentally observed continuous ordering transition, absent from previous models.

cond-mat.str-el↗