arXiv subjects

J. T. Chalker

Publications and source records attributed to J. T. Chalker.

At least 37 records · Page 2Linked to original sources

arXiv2018

Solution of a minimal model for many-body quantum chaos

We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.

cond-mat.stat-mech↗

arXiv2018

Mott, Floquet, and the response of periodically driven Anderson insulators

We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times---which is the physics of Floquet late time states---and strong electric fields. This results in a `phase diagram' in the frequency-field strength plane, in which we identify four distinct regimes. These are: a linear response regime dominated by pre-existing Mott resonances, which exists provided Floquet saturation is not reached within a period; a non-linear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to pre-existing resonances; and finally an enhanced dissipative regime.

cond-mat.dis-nn↗

arXiv2018

Spectral statistics in spatially extended chaotic quantum many-body systems

We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor $K(t)$ analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, $t_{\rm Th}$. We obtain a striking dependence of $t_{\rm Th}$ on the spatial dimension $d$ and size of the system. For $d>1$, $t_{\rm Th}$ is finite in the thermodynamic limit and set by the inter-site coupling strength. By contrast, in one dimension $t_{\rm Th}$ diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form.

cond-mat.stat-mech↗

arXiv2017

Deconfinement transitions in a generalised XY model

We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz-Thouless (KT) transitions for both the half-vortices and ordinary vortices, as well as an Ising-type transition. There also occurs an unusual deconfining phase transition, where the disordered to superfluid transition is of Ising rather than KT type. We show by analytical arguments and extensive numerical simulations that there is a point in the phase diagram where the KT transition line meets the deconfining Ising phase transition. We find that the latter extends into the disordered phase not as a phase transition, but rather solely as a deconfinement transition. It is best understood in the dual height model, where on one side of the transition height steps are bound into pairs while on the other they are unbound. We also extend the phase diagram of the dual model, finding both O(2) loop model and antiferromagnetic Ising transitions.

cond-mat.stat-mech↗

arXiv2016

Coherent hole propagation in an exactly solvable gapless spin liquid

We examine the dynamics of a single hole in the gapless phase of the Kitaev honeycomb model, focusing on the slow-hole regime where the bare hopping amplitude $t$ is much less than the Kitaev exchange energy $J$. In this regime, the hole does not generate gapped flux excitations and is dressed only by the gapless fermion excitations. Investigating the single-hole spectral function, we find that the hole propagates coherently with a quasiparticle weight that is finite but approaches zero as $t/J \to 0$. This conclusion follows from two approximate treatments, which capture the same physics in complementary ways. Both treatments use the stationary limit as an exactly solvable starting point to study the spectral function approximately (i) by employing a variational approach in terms of a trial state that interpolates between the limits of a stationary hole and an infinitely fast hole and (ii) by considering a special point in the gapless phase that corresponds to a simplified one-dimensional problem.

cond-mat.str-el↗

arXiv2016

Classical spin liquids in stacked triangular lattice Ising antiferromagnets

We study Ising antiferromagnets that have nearest-neighbour interactions on multilayer triangular lattices with frustrated ($abc$ and $abab$) stacking, and make comparisons with the unfrustrated ($aaa$) stacking. If interlayer couplings are much weaker than in-plane ones, the paramagnetic phase of models with frustrated stackings has a classical spin-liquid regime at low temperature, in which correlations are strong both within and between planes, but there is no long-range order. We investigate this regime using Monte Carlo simulations and by mapping the spin models to coupled height models, which are treated using renormalisation group methods and an analysis of the effects of vortex excitations. The classical spin-liquid regime is parametrically wide at small interlayer coupling in models with frustrated stackings. By contrast, for the unfrustrated stacking there is no extended regime in which interlayer correlations are strong without three-dimensional order.

cond-mat.stat-mech↗

arXiv2016

Majorana spectroscopy of 3D Kitaev spin-liquids

We analyse the dynamical response of a range of 3D Kitaev quantum spin-liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines or Weyl points. We find that the behaviour of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a non-vanishing density of states, to the phase shifts encountered in the corresponding X-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine-structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalise, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.

cond-mat.str-el↗

arXiv2016

Frustration and Correlations in Stacked Triangular Lattice Ising Antiferromagnets

We study multilayer triangular lattice Ising antiferromagnets with interlayer interactions that are weak and frustrated in an abc stacking. By analysing a coupled height model description of these systems, we show that they exhibit a classical spin liquid regime at low temperature, in which both intralayer and interlayer correlations are strong but there is no long range order. Diffuse scattering in this regime is concentrated on a helix in reciprocal space, as observed for charge-ordering in the materials LuFe$_2$O$_4$ and YbFe$_2$O$_4$.

cond-mat.stat-mech↗

arXiv2015

Long-range Magnetic Order in Models for Rare Earth Quasicrystals

We take a two-step theoretical approach to study magnetism of rare earth quasicrystals by considering Ising spins on quasiperiodic tilings, coupled via RKKY interactions. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on the two-dimensional quasiperiodic tilings. We find that the magnetic interactions are frustrated and strongly dependent on the local environment. This results in the formation of clusters with strong bonds at certain patterns of the tilings that repeat quasiperiodically. Second, we examine the statistical mechanics of Ising spins with these RKKY interactions, using extensive Monte Carlo simulations. Although models that have frustrated interactions and lack translational invariance might be expected to display spin glass behaviour, we show that the spin system has a phase transition to low-temperature states with long-range quasiperiodic magnetic order. Additionally, we find that in some of the systems spin clusters can fluctuate much below the ordering temperature.

cond-mat.str-el↗

arXiv2015

Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition

We show numerically that the `deconfined' quantum critical point between the Néel antiferromagnet and the columnar valence-bond-solid, for a square lattice of spin-1/2s, has an emergent $SO(5)$ symmetry. This symmetry allows the Néel vector and the valence-bond-solid order parameter to be rotated into each other. It is a remarkable 2+1-dimensional analogue of the $SO(4)= [SU(2)\times SU(2)]/Z_2$ symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent $SO(5)$ is strong evidence that the phase transition in the 2+1D system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (non-compact $CP^1$ model). The result indicates that in three dimensions there is an $SO(5)$-symmetric conformal field theory which has no relevant singlet operators, so is radically different to conventional Wilson-Fisher-type conformal field theories.

cond-mat.str-el↗

arXiv2015

Neutron scattering signatures of the 3D hyper-honeycomb Kitaev quantum spin-liquid

Motivated by recent synthesis of the hyper-honeycomb material $β$-$\mathrm{Li_2 Ir O_3}$, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalised degrees of freedom are Majorana fermions and emergent flux-loops. Properties of this 3D model are known to differ in important ways from those of its 2D counterpart -- it has finite-temperature phase transition, as well as distinct features in Raman response. We show, however, that the qualitative behaviour of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs.

cond-mat.str-el↗

arXiv2015

Dynamics of Fractionalization in Quantum Spin Liquids

We present the theory of dynamical spin-response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin-fractionalization into emergent quasiparticles -- Majorana fermions and fluxes of $Z_2$ gauge field. In addition to a broad continuum from spin-fractionalization, we find sharp ($δ$-function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions; and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase.

cond-mat.str-el↗

arXiv2015

Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models

Numerical studies of the Néel to valence-bond solid phase transition in 2D quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realise the universal physics of the Neel-VBS transition in a 3D classical loop model (this includes the interference effect that suppresses Néel hedgehogs). We use this model to simulate unprecedentedly large systems (of size $L\leq 512$). Our results are compatible with a direct continuous transition at which both order parameters are critical, and we do not see conventional signs of first-order behaviour. However, we find that the scaling violations are stronger than previously realised and are incompatible with conventional finite-size scaling over the size range studied, even if allowance is made for a weakly/marginally irrelevant scaling variable. In particular, different determinations of the anomalous dimensions $η_\text{VBS}$ and $η_\text{Néel}$ yield very different results. The assumption of conventional finite-size scaling gives estimates which drift to negative values at large $L$, in violation of unitarity bounds. In contrast, the behaviour of correlators on scales much smaller than $L$ is consistent with large positive anomalous dimensions. Barring an unexpected reversal in behaviour at still larger sizes, this implies that the transition, if continuous, must show unconventional finite-size scaling, e.g. from a dangerously irrelevant scaling variable. Another possibility is an anomalously weak first-order transition. By analysing the renormalisation group flows for the non-compact $CP^{n-1}$ model ($n$-component Abelian Higgs model) between two and four dimensions, we give the simplest scenario by which an anomalously weak first-order transition can arise without fine-tuning of the Hamiltonian.

cond-mat.str-el↗

arXiv2015

Magnetism in Rare Earth Quasicrystals: RKKY Interactions and Ordering

We study magnetism in simple models for rare earth quasicrystals by means of a two-step theoretical approach. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on a two-dimensional quasiperiodic tiling. Second, we examine the statistical mechanics of Ising spins coupled via these interactions using Monte Carlo simulations. We find the emergence of strongly coupled spin clusters with significantly weaker inter-cluster coupling, and a transition to a low-temperature phase that has long-range order evidenced by a finite domain wall tension.

cond-mat.str-el↗

arXiv2014

Doping a topological quantum spin liquid: slow holes in the Kitaev honeycomb model

We present a controlled microscopic study of mobile holes in the spatially anisotropic (Abelian) gapped phase of the Kitaev honeycomb model. We address the properties of (i) a single hole [its internal degrees of freedom as well as its hopping properties]; (ii) a pair of holes [their (relative) particle statistics and interactions]; (iii) the collective state for a finite density of holes. We find that each hole in the doped model has an eight-dimensional internal space, characterized by three internal quantum numbers: the first two "fractional" quantum numbers describe the binding to the hole of the fractional excitations (fluxes and fermions) of the undoped model, while the third "spin" quantum number determines the local magnetization around the hole. The fractional quantum numbers also encode fundamentally distinct particle properties, topologically robust against small local perturbations: some holes are free to hop in two dimensions, while others are confined to hop in one dimension only; distinct hole types have different particle statistics, and in particular, some of them exhibit non-trivial (anyonic) relative statistics. These particle properties in turn determine the physical properties of the multi-hole ground state at finite doping, and we identify two distinct ground states with different hole types that are stable for different model parameters. The respective hopping dimensionalities manifest themselves in an electrical conductivity approximately isotropic in one ground state and extremely anisotropic in the other one. We also compare our microscopic study with related mean-field treatments, and discuss the main discrepancies between the two approaches, which in particular involve the possibility of binding fractional excitations as well as the particle statistics of the holes.

cond-mat.str-el↗

arXiv2013

Phase transitions in 3D loop models and the $CP^{n-1}$ $σ$ model

We consider the statistical mechanics of a class of models involving close-packed loops with fugacity $n$ on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretisations of $CP^{n-1}$ $σ$ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the $σ$ model, and we discuss the relationship between loop properties and $σ$ model correlators. On large scales, loops are Brownian in an ordered phase and have a non-trivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for $n=1,2,3$ and first order transitions for $n\geq 4$. We also give a renormalisation group treatment of the $CP^{n-1}$ model that shows how a continuous transition can survive for values of $n$ larger than (but close to) two, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localisation in symmetry class C, and the statistics of random curves in three dimensions.

cond-mat.stat-mech↗

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

Length Distributions in Loop Soups

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using $CP^{n-1}$ or $RP^{n-1}$ and O(n) $σ$ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter $θ$ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.

cond-mat.stat-mech↗