arXiv subjects

Leon Balents

Publications and source records attributed to Leon Balents.

At least 73 records · Page 4Linked to original sources

arXiv2020

High order magnon bound states in the quasi-one-dimensional antiferromagnet $α$-NaMnO$_2$

Here we report on the formation of two and three magnon bound states in the quasi-one-dimensional antiferromagnet $α$-NaMnO$_2$, where the single-ion, uniaxial anisotropy inherent to the Mn$^{3+}$ ions in this material provides a binding mechanism capable of stabilizing higher order magnon bound states. While such states have long remained elusive in studies of antiferromagnetic chains, neutron scattering data presented here demonstrate that higher order $n>2$ composite magnons exist, and, specifically, that a weak three-magnon bound state is detected below the antiferromagnetic ordering transition of NaMnO$_2$. We corroborate our findings with exact numerical simulations of a one-dimensional Heisenberg chain with easy-axis anisotropy using matrix-product state techniques, finding a good quantitative agreement with the experiment. These results establish $α$-NaMnO$_2$ as a unique platform for exploring the dynamics of composite magnon states inherent to a classical antiferromagnetic spin chain with Ising-like single ion anisotropy.

cond-mat.str-el↗

arXiv2020

Moiré magnets

We introduce a general framework to study moiré structures of two-dimensional Van der Waals magnets using continuum field theory. The formalism eliminates quasiperiodicity and allows a full understanding of magnetic structures and their excitations. In particular, we analyze in detail twisted bilayers of Néel antiferromagnets on the honeycomb lattice. A rich phase diagram with non-collinear twisted phases is obtained, and spin waves are further calculated. Direct extensions to zig-zag antiferromagnets and ferromagnets are also presented. We anticipate the results and formalism presented to lead to a broad range of applications to both fundamental research and experiments.

cond-mat.mes-hall↗

arXiv2020

Collective spinon spin wave in a magnetized U(1) spin liquid

We study the transverse dynamical spin susceptibility of the two dimensional U(1) spinon Fermi surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed non-interacting spinon approximation. Short-range interaction leads to a new collective mode: a "spinon spin wave" which splits off from the two-spinon continuum at small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing non-zero power law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as $B^{2/3}$ with magnetic field $B$ at low temperature. Our results form the basis for a theory of inelastic neutrons scattering, ESR, and resonant inelastic x-ray scattering (RIXS) studies of this quantum spin liquid state.

cond-mat.str-el↗

arXiv2019

Optical excitation of magnons in an easy-plane antiferromagnet: Application to Sr$_2$IrO$_4$

We study the interaction of a (classical) light field with the magnetic degrees of freedom in the two-dimensional antiferromagnet Sr$_2$IrO$_4$. The reduced space group symmetry of the crystal allows for several channels for spin-operator bilinears to couple to the electric field. Integrating out high-energy degrees of freedom in a Keldysh framework, we derive induced effective fields which enter the equations of motion of the low-energy mode of in-plane rotations which couple to the out-of-plane magnetization. Considering a pump-probe protocol, these induced fields excite magnetization oscillations which can subsequently probed, e.g. using Kerr rotation. We discuss how the induced fields depend on polarization and frequency of the driving light, and our study applies to both resonant and non-resonant regimes. Crucially, the induced fields depend on the two-magnon density of states, thus allowing for further insight into properties of the magnetic excitation spectrum. Furthermore, these effects rely upon (weak) magnon-interactions, and so are beyond a "Floquet magnon" description.

cond-mat.str-el↗

arXiv2019

General continuum model for twisted bilayer graphene and arbitrary smooth deformations

We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer grapheneas well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

cond-mat.mes-hall↗

arXiv2019

Chiral domain walls of Mn$_3$Sn and their memory

Magnetic domain walls are topological solitons whose internal structure is set by competing energies which sculpt them. In common ferromagnets, domain walls are known to be of either Bloch or Néel types. Little is established in the case of Mn$_3$Sn, a triangular antiferromagnet with a large room-temperature anomalous Hall effect, where domain nucleation is triggered by a well-defined threshold magnetic field. Here, we show that the domain walls of this system generate an additional contribution to the Hall conductivity tensor and a transverse magnetization. The former is an electric field lying in the same plane with the magnetic field and electric current and therefore a planar Hall effect. We demonstrate that in-plane rotation of spins inside the domain wall would explain both observations and the clockwise or anticlockwise chirality of the walls depends on the history of the field orientation and can be controlled.

cond-mat.str-el↗

arXiv2019

Competing orders in pyrochlore magnets from a $\mathbb{Z}_2$ spin liquid perspective

The pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-range-entangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled $\mathbb{Z}_2$ spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic spinons. For each spin liquid, we construct a mean-field Hamiltonian that can be used to describe phase transitions out of the spin liquid via spinon condensation. Studying these phase transitions, we establish phase diagrams for our mean-field Hamiltonians that link magnetic orders to specific spin liquids. In general, we find that seemingly unrelated magnetic orders are intertwined with each other and that the conventional spin orders seen in the experiments are accompanied by more exotic hidden orders. Our critical theories are categorized into $z=1$ and $z=2$ types, based on their spinon dispersion and Hamiltonian diagonalizability, and are shown to give distinct signatures in the heat capacity and the spin structure factor. This study provides a clear map of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.

cond-mat.str-el↗

arXiv2019

Landau levels in twisted bilayer graphene and semiclassical orbits

Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1$^\circ$. This is now strongly supported by experiment, which furthermore reveals dramatic correlation effects in the magic range due to the relative dominance of interactions when the bandwidth is suppressed. Experimentally, quantum oscillations exhibit different Landau level degeneracies when the angles fall in or outside the magic range; these observations can contain crucial information about the low energy physics. In this paper, we report a thorough theoretical study of the Landau level structure of the non-interacting continuum model for twisted bilayer graphene as the magnetic field and the twist angle are tuned. We first show that a discernible difference exists in the butterfly spectra when twist angle falls in and outside the magic range. Next, we carry out semiclassical analysis in detail, which quantitatively determines the origin of the low energy Landau levels from the zero field band structure. We find that the Landau level degeneracy predicted in the above analyses is capable of partially explaining features of the quantum oscillation experiments in a natural way. Finally, topological aspects, validity, and other subtle points of the model are discussed.

cond-mat.str-el↗

arXiv2018

Multiple topological transitions in twisted bilayer graphene near the first magic angle

Recent experiments have observed strongly correlated physics in twisted bilayer graphene (TBG) at very small angles, along with nearly flat electron bands at certain fillings. A good starting point in understanding the physics is a continuum model (CM) proposed by Lopes dos Santos et al. [Phys. Rev. Lett. 99, 256802 (2007)] and Bistritzer et al. [PNAS 108, 12233 (2011)] for TBG at small twist angles, which successfully predicts the bandwidth reduction of the middle two bands of TBG near the first magic angle $θ_0=1.05^\circ$. In this paper, we analyze the symmetries of the CM and investigate the low energy flat band structure in the entire moiré Brillouin zone near $θ_0$. Instead of observing flat bands at only one "magic" angle, we notice that the bands remain almost flat within a small range around $θ_0$, where multiple topological transitions occur. The topological transitions are caused by the creation and annihilation of Dirac nodes at either $\text{K}$, $\text{K}^\prime$, or $Γ$ points, or along the high symmetry lines in the moiré Brillouin zone. We trace the evolution of the nodes and find that there are several processes transporting them from $Γ$ to $\text{K}$ and $\text{K}^\prime$. At the $Γ$ point, the lowest energy levels of the CM are doubly degenerate for some range of twisting angle around $θ_0$, suggesting that the physics is not described by any two band model. Based on this observation, we propose an effective six-band model (up to second order in quasi-momentum) near the $Γ$ point with the full symmetries of the CM, which we argue is the minimal model that explains the motion of the Dirac nodes around $Γ$ as the twist angle is varied. By fitting the coefficients from the numerical results, we show that this six-band model captures the important physics over a wide range of angles near the first "magic" angle.

cond-mat.str-el↗

arXiv2018

Amplitude mode in the planar triangular antiferromagnet Na$_{0.9}$MnO$_2$

Amplitude modes arising from symmetry breaking in materials are of broad interest in condensed matter physics. These modes reflect an oscillation in the amplitude of a complex order parameter, yet are typically unstable and decay into oscillations of the order parameter's phase. This renders stable amplitude modes rare, and exotic effects in quantum antiferromagnets have historically provided a realm for their detection. Here we report an alternate route to realizing amplitude modes in magnetic materials by demonstrating that an antiferromagnet on a two-dimensional anisotropic triangular lattice ($α$-Na$_{0.9}$MnO$_2$) exhibits a long-lived, coherent oscillation of its staggered magnetization field. Our results show that geometric frustration of Heisenberg spins with uniaxial single-ion anisotropy can renormalize the interactions of a dense two-dimensional network of moments into largely decoupled, one-dimensional chains that manifest a longitudinally polarized bound state. This bound state is driven by the Ising-like anisotropy inherent to the Mn$^{3+}$ ions of this compound.

cond-mat.str-el↗

arXiv2018

Quantization of the thermal Hall conductivity at small Hall angles

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity $κ_{xx}$ due to phonons is much larger than the expected quantized thermal Hall conductance $κ_{xy}^{\rm q}=\frac{πT}{12} \frac{k_B^2}{\hbar}$ of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an {\em effective} Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length $L \gg \ell$, where $\ell$ is a thermalization length. We obtain $\ell \sim T^{-5}$ for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, $κ_{xy}/κ_{xx} \sim 10^{-3}$, in $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2018

Floquet spin and spin-orbital Hamiltonians and doublon-holon generations in periodically driven Mott insulators

We consider Mott insulators driven by periodic coherent laser radiation, using both single orbital and multi-orbital models, noting that the latter is of more interest in solid state systems. We derive general expressions for the resulting periodically driven spin models and spin-orbital models using time-dependent perturbation theory. First, we show that the effective exchange interactions of the Floquet Hamiltonians are highly tunable by the frequency, amplitude, and polarization of the laser. Second, we take the effect of finite bandwidth of excitations into account and study possible heating effects. Using the same formalism with a slight modification we also consider the small frequency regime and study the dielectric breakdown of Mott insulators.

cond-mat.str-el↗

arXiv2018

Quantum Entanglement of the Sachdev-Ye-Kitaev Models

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model of fermions interacting with $q$-body random couplings. For $q=2$, it describes free particles, and is non-chaotic in the many-body sense, while for $q>2$ it is strongly interacting and exhibits many-body chaos. In this work we study the entanglement entropy (EE) of the SYK$q$ models, for a bipartition of $N$ real or complex fermions into subsystems containing $2m$ real/$m$ complex fermions and $N-2m$/$N-m$ fermions in the remainder. For the free model SYK$2$, we obtain an analytic expression for the EE, derived from the $β$-Jacobi random matrix ensemble. Furthermore, we use the replica trick and path integral formalism to show that the EE is {\em maximal} for when one subsystem is small, i.e. $m\ll N$, for {\em arbitrary} $q$. We also demonstrate that the EE for the SYK4 model is noticeably smaller than the Page value when the two subsystems are comparable in size, i.e. $m/N$ is $O(1)$. Finally, we explore the EE for a model with both SYK2 and SYK4 interaction and find a crossover from SYK2 (low temperature) to SYK4 (high temperature) behavior as we vary energy.

cond-mat.str-el↗

arXiv2018

Suppressed Density of States in Self-Generated Coulomb Glasses

We investigate the structure of metastable states in self-generated Coulomb glasses. In dramatic contrast to disordered electron glasses, we find that these states lack marginal stability. Such absence of marginal stability is reflected by the suppression of the single-particle density of states into an exponentially soft gap of the form $g(ε) \sim e^{-V / ξ|ε|}$. To analytically explain this behavior, we extend the stability criterion of Efros and Shklovskii to incorporate local charge correlations, in qualitative agreement with our numerical findings. Our work suggests the existence of a new class of self-generated glasses dominated by strong geometric frustration.

cond-mat.stat-mech↗

arXiv2018

Finite-temperature behavior of a classical spin-orbit-coupled model for $\textrm{YbMgGaO}_4$ with and without bond disorder

We present the results of finite-temperature classical Monte Carlo simulations of a strongly spin-orbit-coupled nearest-neighbor triangular-lattice model for the candidate $\mathrm{U}(1)$ quantum spin liquid $\mathrm{YbMgGaO}_4$ at large system sizes. We find a single continuous finite-temperature stripe-ordering transition with slowly diverging heat capacity that completely breaks the sixfold ground-state degeneracy, despite the absence of a known conformal field theory describing such a transition. We also simulate the effect of random-bond disorder in the model, and find that even weak bond disorder destroys the transition by fragmenting the system into very large domains -- possibly explaining the lack of observed ordering in the real material. The Imry-Ma argument only partially explains this fragility to disorder, and we extend the argument with a physical explanation for the preservation of our system's time-reversal symmetry even under a disorder model that preserves the same symmetry.

cond-mat.str-el↗

arXiv2018

Topological Superconductivity in Twisted Multilayer Graphene

We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat mini-band resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the nature of thepreferred pairing states, favoring spin triplet $d+id$ order with a valley singlet structure. We identify two candidates in this class, which are both topological superconductors. These states support half-vortices carrying half the usual superconducting flux quantum $hc/(4e)$, and have topologically protected gapless edge states.

cond-mat.str-el↗

arXiv2018

Fracton topological phases from strongly coupled spin chains

We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines or planes. We demonstrate that a wide range of these fracton phases can be constructed by strongly coupling mutually intersecting spin chains and explain via a concrete example how such a coupled-spin-chain construction illuminates the generic properties of a fracton phase. In particular, we describe a systematic translation from each coupled-spin-chain construction into a parton construction where the partons correspond to the excitations that are mobile along lines. Remarkably, our construction of fracton phases is inherently based on spin models involving only two-spin interactions and thus brings us closer to their experimental realization.

cond-mat.str-el↗

arXiv2018

Classical Discrete Time Crystals

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions, and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator-prey models to Faraday waves and AC-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially-long time scales. Power-law correlations are present along a first-order line which terminates at a critical point. We analyze the transition by mapping it to the locked-to-sliding transition of a DC-driven charge density wave. Our work points to a classical limit for quantum time crystals, and raises several intriguing questions concerning the non-equilibrium universality class of the CDTC critical point.

cond-mat.stat-mech↗