arXiv subjects

Xiangyu Cao

Publications and source records attributed to Xiangyu Cao.

At least 37 records · Page 2Linked to original sources

arXiv2021

Quasiparticle kinetic theory for Calogero models

We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe-Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.

cond-mat.stat-mech↗

arXiv2021

Gate-tunable Intrinsic Anomalous Hall Effect in Epitaxial MnBi2Te4 Films

Anomalous Hall effect (AHE) is an important transport signature revealing topological properties of magnetic materials and their spin textures. Recently, antiferromagnetic MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator that exhibits quantum AHE in exfoliated nanoflakes. However, its complicated AHE behaviors may offer an opportunity for the unexplored correlation between magnetism and band structure. Here, we show the Berry curvature dominated intrinsic AHE in wafer-scale MnBi2Te4 thin films. By utilizing a high-dielectric SrTiO3 as the back-gate, we unveil an ambipolar conduction and electron-hole carrier (n-p) transition in ~7 septuple layer MnBi2Te4. A quadratic relation between the saturated AHE resistance and longitudinal resistance suggests its intrinsic AHE mechanism. For ~3 septuple layer MnBi2Te4, however, the AHE reverses its sign from pristine negative to positive under the electric-gating. The first-principles calculations demonstrate that such behavior is due to the competing Berry curvature between polarized spin-minority-dominated surface states and spin-majority-dominated inner-bands. Our results shed light on the physical mechanism of the gate-tunable intrinsic AHE in MnBi2Te4 thin films and provide a feasible approach to engineering its AHE.

cond-mat.mtrl-sci↗

arXiv2021

A statistical mechanism for operator growth

It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in $d \ge 2$ dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.

cond-mat.stat-mech↗

arXiv2021

Level Set Percolation in Two-Dimensional Gaussian Free Field

The nature of level set percolation in the two-dimension Gaussian Free Field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition, and characterize the critical point. In particular, the correlation length diverges exponentially, and the critical clusters are "logarithmic fractals", whose area scales with the linear size as $A \sim L^2 / \sqrt{\ln L}$. The two-point connectivity also decays as the log of the distance. We corroborate our theory by numerical simulations. Possible CFT interpretations are discussed.

cond-mat.stat-mech↗

arXiv2021

Giant nonlinear anomalous Hall effect induced by spin-dependent band structure evolution

Anomalous Hall effect (AHE) is the key transport signature unlocking topological properties of magnetic materials. While AHE is usually proportional to the magnetization, the nonlinearity suggests the existence of complex magnetic and electron orders. Nonlinear AHE includes the topological Hall effect (THE) that has been widely used to identify the presence of spin chirality in real space. But it can in principle be induced by band structure evolution via Berry curvatures in the reciprocal space. This effect has been largely overlooked due to the intertwined mechanisms in both real and reciprocal spaces. Here, we observed a giant nonlinear AHE with the resistivity up to 383.5 uohm cm, contributing unprecedentedly 97% of the total Hall response in EuCd2As2. Moreover, it can be further enhanced by tilting the magnetic field 30° away from [001] direction, reaching a large anomalous Hall angle up to 21%. Although it shows exactly the same double-peak feature as THE, our scaling analysis and first-principles calculations reveal that the Berry phase is extremely sensitive to the spin canting, and nonlinear AHE is a consequence of band structure evolution under the external magnetic fields. When the spins gradually tilt from the in-plane antiferromagnetic ground state to out-of-plane direction, band crossing and band inversion occur, introducing a bandgap at Γ point at a canting angle of 45°. That contributes to the enhancement of Berry curvature and consequently a large intrinsic Hall conductivity. Our results unequivocally reveal the sensitive dependence of band structures on spin tilting process under external magnetic fields and its pronounced influence on the transport properties, which also need to be taken into consideration in other magnetic materials.

cond-mat.mtrl-sci↗

arXiv2021

Comment on "Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model"

In arXiv:1707.02197, the authors considered the Sachdev-Ye-Kitaev model with quadratic perturbation (also known as mass-deformed SYK), and claimed that the quantum Lyapunov exponent would vanish in the regime of low temperature and small quartic coupling. We calculate the exponent exactly in that regime and show that it is nonzero.

cond-mat.stat-mech↗

arXiv2021

Dirac Fast Scramblers

We introduce a family of Gross-Neveu-Yukawa models with a large number of fermion and boson flavors as higher dimensional generalizations of the Sachdev-Ye-Kitaev model. The models may be derived from local lattice couplings and give rise to Lorentz invariant critical solutions in 1+1 and 2+1 dimensions. These solutions imply anomalous dimensions of both bosons and fermions tuned by the number ratio of boson to fermion flavors. In 1+1 dimension the solution represents a stable critical phase, while in 2+1 dimension it governs a quantum phase transition. We compute the out of time order correlators in the 1+1 dimensional model, showing that it exhibits growth with the maximal Lyapunov exponent $λ_L=2πT$ in the low temperature limit.

cond-mat.str-el↗

arXiv2021

Origin and Limit of the Recovery of Damaged Information by Time Reversal

Recently it was found that scrambled information can be partially recovered by a time-reversed evolution, even after being damaged by an intruder. We reconsider the origin of the information recovery, and argue that the presence of classical chaos does not preclude it and only leads to a quantitative reduction of the recovery ratio. We also show how decoherence (i.e. entanglement with the intruder) limits the recovery, by proving an upper bound on the recovery ratio in terms of the entangling power of the intruder's action.

quant-ph↗

arXiv2020

Local Matrix Product Operators: Canonical Form, Compression, & Control Theory

We present a new method for compressing matrix product operators (MPOs) which represent sums of local terms, such as Hamiltonians. Just as with area law states, such local operators may be fully specified with a small amount of information per site. Standard matrix product state (MPS) tools are ill-suited to this case, due to extensive Schmidt values that coexist with intensive ones, and Jordan blocks in the transfer matrix. We ameliorate these issues by introducing an "almost Schmidt decomposition" that respects locality. Our method is "$\varepsilon$-close" to the accuracy of MPS-based methods for finite MPOs, and extends seamlessly to the thermodynamic limit, where MPS techniques are inapplicable. In the framework of control theory, our method generalizes Kung's algorithm for model order reduction. Several examples are provided, including an all-MPO version of the operator recursion method (Lanczos algorithm) directly in the thermodynamic limit. All results are accompanied by practical algorithms, well-suited for the large MPOs that arise in DMRG for long-range or quasi-2D models.

cond-mat.str-el↗

arXiv2020

Scrambling versus relaxation in Fermi and non-Fermi liquids

We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $N$, allows us to clarify the relations between the quasi-particle relaxation rate $1/τ$ and the Lyapunov exponent $λ_L$ characterizing scrambling. In the Fermi liquid states we find that the quasi-particle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/τ\gg T$, we find that $λ_L$ is always $T$-linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. $λ_L$ approaches the general upper bound $2πT$ at the transition to a fast scrambling state. Finally in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a non analytic function $\sim g \ln (1/g)$ of the coupling constant $g$.

cond-mat.str-el↗

arXiv2020

Does scrambling equal chaos?

Focusing on semiclassical systems, we show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

cond-mat.stat-mech↗

arXiv2020

Low-rank Sachdev-Ye-Kitaev models

Motivated by recent works on atom-cavity realizations of fast scramblers, and on Cooper pairing in non-Fermi liquids, we study a family of solvable variants of the ($q=4$) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate {an extensively degenerate or negative semidefinite coupling matrix}. More generic distributions give rise to "almost Fermi liquids" with a scaling dimension $Δ= 1/2$, but which differ from a genuine Fermi-liquid in quasi-particle decay rate, quantum Lyapunov exponent and/or specific heat.

cond-mat.str-el↗

arXiv2019

The GGE averaged currents of the classical Toda chain

The Toda chain with random initial data is studied. Of particular interest are generalized Gibbs ensembles, their averaged conserved fields, and the averages of the corresponding currents. While averaged fields are well-understood, the description of averaged currents has hitherto relied on the collision-rate assumption. For the Toda chain, the rate assumption can be investigated numerically. Here, we provide convincing evidence for the validity of the rate assumption. This lends further support to the idea that generalized Euler-type equations have a structure common to all integrable extensive systems.

cond-mat.stat-mech↗

arXiv2019

A Universal Operator Growth Hypothesis

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate $α$ in generic systems, with an extra logarithmic correction in 1d. The rate $α$ --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-$N$ limits. Moreover, $α$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents $λ_L \leq 2 α$, which complements and improves the known universal low-temperature bound $λ_L \leq 2 πT$. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.

cond-mat.stat-mech↗

arXiv2019

Integrable and chaotic dynamics of spins coupled to an optical cavity

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop `dressing tails' of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-$S$ limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in light of the limitations set by cavity dissipation.

cond-mat.stat-mech↗

arXiv2019

Entanglement in a fermion chain under continuous monitoring

We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.

cond-mat.stat-mech↗

arXiv2019

Kinetic theory of quantum and classical Toda lattices

We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the kinetic theory depends smoothly on Planck's constant, and explicitly characterise the leading quantum corrections to classical behaviour. The classical kinetic theory is compared with direct numerical simulations and shows excellent agreement. Finally, we connect the Bethe-Boltzmann approach with the classical inverse scattering method, by identifying conserved quasiparticles with the spectrum of the Lax matrix.

cond-mat.stat-mech↗

arXiv2018

Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like `impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.

cond-mat.dis-nn↗