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In recent years, twisted bilayer systems such as bilayer graphene have attracted a great deal of attention as the twist angle introduces a degree of freedom which can be used to non-trivially modify system properties. This idea has been picked up in the cold atom community, first with a theoretical proposal to simulate twisted bilayers in state-dependent optical lattices, and, more recently, with an experimental realization of twisted bilayers with bosonic atoms in two different spin states. In this manuscript, we theoretically investigate dipolar bosons in a twisted bilayer geometry. The interplay between dipolar interaction and the twist between the layers results in the emergence of quantum states not observed in the absence of twist. We study how system properties vary as we change the twist angle at fixed distance between the layers and fixed dipolar interaction. We find that at a twist angle $\theta=0.1^{\circ}$, the observed quantum phases are consistent with those seen in the absence of twist angle, i.e. paired superfluid, paired supersolid, and paired solid phases. However, a slight increase in the twist angle to $\theta=0.2^{\circ}$ disrupts these paired phases in favor of a phase separation between checkerboard solid and superfluid regions. Notably, at a twist angle of $\theta=5.21^{\circ}$, the local occupation number follows the moir\'e pattern of the underlying moir\'e bilayers so that a periodic structure of insulating islands is formed. These insulating islands are surrounded by a superfluid., Comment: 6 pages, 4 figures

Finding accurate ground state energy of a many-body system has been a major challenge in quantum chemistry. The integration of classic and quantum computers has shed new light on resolving this outstanding problem. Here we propose QiankunNet-VQE, a transformer based language models enforced with quantum computing to learn and generate quantum states. It has been implemented using up to 12 qubits and attaining an accuracy level competitive with state-of-the-art classical methods. By leveraging both quantum and classical resources, this scheme overcomes the limitations of variational quantum eigensolver(VQE) without the need for cumbersome error mitigation. Moreover, QiankunNet-VQE provides a different route to achieve a practical quantum advantage for solving many-electron Schr\"odinger equation without requiring extremely precise preparation and measurement of the ground-state wavefunction on quantum computer.

The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of long-range interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction $\sim1/r^{2+\sigma}$. Utilizing an advanced update strategy, we conduct large-scale Monte Carlo simulations of the model up to a linear size of $L=8192$. Our results demonstrate continuous phase transitions into a ferromagnetic phase for $\sigma \leq 2$, which exhibits the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at $\sigma = 2$. The observed scaling behaviors in the low-temperature phase for $\sigma \le 2$ agree with our theoretical analysis. Our findings request further theoretical understandings and can be of practical application in cutting-edge experiments like Rydberg atom arrays.

Let $\Delta_\lambda$ be the Bessel operator on the upper half space $\mathbb{R}_+^{n+1}$ with $n\geq 0$ and $\lambda>0$, and $R_{\lambda,j}$ be the $j-$th Bessel Riesz transform, $j=1,\ldots,n+1$. We demonstrate that the Schatten--Lorentz norm ($S^{p,q}$, $1

The proliferation of topological defects is a common out-of-equilibrium phenomenon when a system is driven into a phase of broken symmetry. The Kibble-Zurek mechanism (KZM) provides a theoretical framework for the critical dynamics and generation of topological defects in such scenarios. One of the early applications of KZM is the estimation of heavy magnetic monopoles left behind by the cosmological phase transitions in the early universe. The scarcity of such relic monopoles, which contradicts the prediction of KZM, is one of the main motivations for cosmological inflationary theories. On the other hand, magnetic monopoles as emergent quasi-particles have been observed in spin ices, a peculiar class of frustrated magnets that remain disordered at temperatures well below the energy scale of exchange interaction. Here we study the annihilation dynamics of magnetic monopoles when spin ice is cooled to zero temperature in a finite time. Through extensive Glauber dynamics simulations, we find that the density of residual monopole follows a power law dependence on the annealing rate. A kinetic reaction theory that precisely captures the annihilation process from Monte Carlo simulations is developed. We further show that the KZM can be generalized to describe the critical dynamics of spin ice, where the exponent of the power-law behavior is determined by the dynamic critical exponent $z$ and the cooling protocol., Comment: 13 pages, 7 figures

Kagome spin ice is one of the canonical examples of highly frustrated magnets. The effective magnetic degrees of freedom in kagome spin ice are Ising spins residing on a two-dimensional network of corner-sharing triangles. Due to strong geometrical frustration, nearest-neighbor antiferromagnetic interactions on the kagome lattice give rise to a macroscopic number of degenerate classical ground states characterized by ice rules. Elementary excitations at low temperatures are defect-triangles that violate the ice rules and carry an additional net magnetic charge relative to the background. We perform large-scale Glauber dynamics simulations to study the nonequilibrium dynamics of kagome ice under slow cooling. We show that the density of residual charge defects exhibits a power law dependence on the quench rate for the class of algebraic cooling protocols. The numerical results are well captured by the rate equation for the charge defects based on the reaction kinetics theory. As the relaxation time of the kagome ice phase remains finite, there is no dynamical freezing as in the Kibble-Zurek scenario. Instead, we show that the power-law behavior originates from a thermal excitation that decay algebraically with time at the late stage of the cooling schedule. Similarities and differences in quench dynamics of other spin ice systems are also discussed., Comment: 8 pages, 4 figures

Reconfigurable intelligent surfaces (RISs) have become one of the key technologies in 6G wireless communications. By configuring the reflection beamforming codebooks, RIS focuses signals on target receivers. In this paper, we investigate the codebook configuration for 1-bit RIS-aided systems. We propose a novel learning-based method built upon the advanced methodology of implicit neural representations. The proposed model learns a continuous and differentiable coordinate-to-codebook representation from samplings. Our method only requires the information of the user's coordinate and avoids the assumption of channel models. Moreover, we propose an encoding-decoding strategy to reduce the dimension of codebooks, and thus improve the learning efficiency of the proposed method. Experimental results on simulation and measured data demonstrated the remarkable advantages of the proposed method.

Simulating long-range interacting systems is a challenging task due to its computational complexity that the computational effort for each local update is of order $\cal{O}$$(N)$, where $N$ is the size of system. Recently, a technique, called hereby the clock factorized quantum Monte Carlo method, was developed on the basis of the so-called factorized Metropolis filter [Phys. Rev. E 99 010105 (2019)]. In this work, we first explain step by step how the clock factorized quantum Monte Carlo method is implemented to reduce the computational overhead from $\cal{O}$$(N)$ to $\cal{O}$(1). In particular, the core ingredients, including the concepts of bound probabilities and bound rejection events, the tree-like data structure, and the fast algorithms for sampling an extensive set of discrete and small probabilities, are elaborated. Next, we show how the clock factorized quantum Monte Carlo method can be flexibly implemented in various update strategies, like the Metropolis and worm-type algorithms, and can be generalized to simulate quantum systems. Finally, we demonstrate the high efficiency of the clock factorized quantum Monte Carlo algorithms in the examples of the quantum Ising model and the Bose-Hubbard model with long-range interactions and/or long-range hopping amplitudes. We expect that the clock factorized quantum Monte Carlo algorithms would find broad applications in statistical and condensed-matter physics.

In this article, we establish sharp endpoint $L_p$ estimates of Schr\"odinger groups on general measure spaces which may not be equipped with good metrics but admit submarkovian semigroups satisfying purely algebraic assumptions. One of the key ingredients of our proof is to introduce and investigate a new noncommutative high-cancellation BMO space by constructing an abstract form of P-metric codifying some sort of underlying metric and position. This provides the first form of Schr\"odinger group theory on arbitrary von Neumann algebras and can be applied to many models, including Schr\"odinger groups associated with non-negative self-adjoint operators satisfying purely Gaussian upper bounds on doubling metric spaces, standard Schr\"odinger groups on quantum Euclidean spaces, matrix algebras and group von Neumann algebras with finite dimensional cocycles., Comment: 50 pages

This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator $\Delta_N$ on $\mathbb R^n$. Along the line of singular value estimates for Riesz transform commutators established by Janson--Wolff and Rochberg--Semmes, we establish a full range of Schatten-$p$ class characterization for these commutators.

A large part of the theory of Hardy spaces on products of Euclidean spaces has been extended to the setting of products of stratified Lie groups. This includes characterisation of Hardy spaces by square functions and by atomic decompositions, proof of the duality of Hardy spaces with BMO, and description of many interpolation spaces. Until now, however, two aspects of the classical theory have been conspicuously absent: the characterisation of Hardy spaces by singular integrals (of Christ--Geller type) or by (vertical or nontangential) maximal functions. In this paper we fill in these gaps by developing new techniques on products of stratified groups, using the ideas of Chen, Cowling, Lee, Li and Ottazzi on the Heisenberg group with flag structure., Comment: Minor corrections and improvements made

We present a new quantum molecular dynamics (MD) method where the electronic structure and atomic forces are solved by a real-space dynamical mean-field theory (DMFT). Contrary to most quantum MD methods that are based on effective single-particle wave functions, the DMFT approach is able to describe correlation-induced Mott metal-insulator transitions and the associated incoherent electronic excitations in an atomic liquid. We apply the DMFT-MD method to study Mott transitions in an atomic liquid model which can be viewed as the liquid-state generalization of the Hubbard model. The half-filled Hubbard liquids also provide a minimum model for alkali fluid metals. Our simulations uncover two distinct types of Mott transition depending on the atomic bonding and short-range structures in the electronically delocalized phase. In the first scenario where atoms tend to form dimers, increasing the Hubbard repulsion gives rise to a transition from a molecular insulator to an atomic insulator with a small window of enhanced metallicity in the vicinity of the localization transition. On the other hand, for Hubbard liquids with atoms forming large conducting clusters, the localization of electrons leads to the fragmentation of clusters and is intimately related to the liquid-gas transition of atoms. Implications of our results for metal-insulator transitions in fluid alkali metals are discussed., Comment: 23 pages, 14 figures

Along the line of singular value estimates for commutators by Rochberg-Semmes, Lord-McDonald-Sukochev-Zanin and Fan-Lacey-Li, we establish the endpoint weak Schatten class estimate for commutators of Riesz transforms with multiplication operator $M_f$ on Heisenberg groups via homogeneous Sobolev norm of the symbol $f$. The new tool we exploit is the construction of a singular trace formula on Heisenberg groups, which, together with the use of double operator integrals, allows us to bypass the use of Fourier analysis and provides a solid foundation to investigate the singular values estimates for similar commutators in general stratified Lie groups., Comment: 48 pages

We study commutators with the Riesz transforms on the Heisenberg group. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson--Wolff and Rochberg--Semmes. The method of proof extends the earlier methods, allowing us to address not just the Riesz transforms, but also the Cauchy--Szego projection and second order Riesz transforms on the Heisenberg group, among other settings., Comment: 23 pages. V2 has shorter proofs

We show that a magnetic field in the high-symmetry direction lifts the macroscopic classical ground-state degeneracy of the honeycomb $\Gamma$ model and induces a long-range magnetic order. While a simple spin-polarized state is stabilized for the ferromagnetic $\Gamma$-exchange, a periodic $\sqrt{3}\times \sqrt{3}$ magnetic order is selected by magnetic field for the antiferromagnetic interaction. We show that the complex spin structure of the tripled unit cell can be described by the magnetization vector and a N\'eel order parameter, similar to those for the spin-flop state of a bipartite antiferromagnet. Indeed, the transition from the low-field plaquette-ordered spin liquid to the field-induced magnetic order can be viewed as a generalized spin-flop transition. An accidental O(2) degeneracy associated with rotation symmetry of the N\'eel vector is broken by either quantum or thermal fluctuations, leaving a six-fold degenerate ground state. At high fields, the breaking of the ground-state $Z_6$ symmetry is through two Berezinskii-Kosterlitz-Thouless transitions that enclose a critical XY phase., Comment: 6 pages, 5 figures

The leading order nonlinear (NL) susceptibility, $\chi_3$, in a paramagnet is negative and diverges as $T \rightarrow 0$. This divergence is destroyed when spins correlate and the NL response provides unique insights into magnetic order. Dimensionality, exchange interaction, and preponderance of quantum effects all imprint their signatures in the NL magnetic response. Here, we study the NL susceptibilities in the proximate Kitaev magnet $\alpha$-RuCl$_3$ which differs from the expected antiferromagnetic behavior. For $T< T_c$ = 7.5 K and field $B$ in the ab-plane, we obtain contrasting NL responses in low ($<$ 2 ${T}$) and high field regions. For low fields the NL behavior is dominated by a quadratic response (positive $\chi_2$), which shows a rapid rise below $T_c$. This large $\chi_2 >0$ implies a broken sublattice symmetry of magnetic order at low temperatures. Classical Monte Carlo (CMC) simulations in the standard ${K-H-\Gamma}$ model secure such a quadratic ${B}$ dependence of ${M}$, only for ${T}$ $\approx$ ${T}_c$ with ${\chi}_2$ being zero as ${T}$ $\rightarrow$ 0. It is also zero for all temperatures in exact diagonalization calculations. On the other hand, we find an exclusive cubic term (${\chi}_3$) describes the high field NL behavior well. ${\chi}_3$ is large and positive both below and above ${T}_c$ crossing zero only for ${T}$ $>$ 50 K. In contrast, for $B$~$\parallel$~c-axis, no separate low/high field behaviors is measured and only a much smaller ${\chi}_3$ is apparent., Comment: Accepted NPJ Quantum Materials

We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink number distribution to assess adiabaticity and its breakdown. We consider linear, nonlinear, and exponential cooling schedules, among which the latter provides the most efficient shortcuts to cooling in a given quench time. The non-thermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state., Comment: 24 pages, 11 figures

In this paper, we study the $L^{p}$ boundedness and $L^{p}(w)$ boundedness ($1\mathbb{Q}/\alpha$, then for any $1

In this paper, we study weighted $L^{p}(w)$ boundedness ($1

Let $L$ be a non-negative self-adjoint operator acting on $L^2(X)$, where $X$ is a space of homogeneous type with a dimension $n$. Suppose that the heat operator $e^{-tL}$ satisfies the generalized Gaussian $(p_0, p'_0)$-estimates of order $m$ for some $1\leq p_0 < 2$. It is known that the operator $(I+L)^{-s } e^{itL}$ is bounded on $L^p(X)$ for $s\geq n|{1/ 2}-{1/p}| $ and $ p\in (p_0, p_0')$ (see for example, \cite{Blunck2, BDN, CCO, CDLY, DN, Mi1}). In this paper we study the endpoint case $p=p_0$ and show that for $s_0= n\big|{1\over 2}-{1\over p_0}\big|$, the operator $(I+L)^{-{s_0}}e^{itL} $ is of weak type $(p_{0},p_{0})$, that is, there is a constant $C>0$, independent of $t$ and $f$ so that \begin{eqnarray*} \mu\left(\left\{x: \big|(I+L)^{-s_0}e^{itL} f(x)\big|>\alpha \right\} \right)\leq C (1+|t|)^{n(1 - {p_0\over 2}) } \left( {\|f\|_{p_0} \over \alpha} \right)^{p_0} , \ \ \ t\in{\mathbb R} \end{eqnarray*} for $\alpha>0$ when $\mu(X)=\infty$, and $\alpha>\big(\|f\|_{p_{0}}/\mu(X) \big)^{p_{0}}$ when $\mu(X)<\infty$. Our results can be applied to Schr\"odinger operators with rough potentials and %second order elliptic operators with rough lower order terms, or higher order elliptic operators with bounded measurable coefficients although in general, their semigroups fail to satisfy Gaussian upper bounds., Comment: 17 pages

Let $L$ be a non-negative self-adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type with a dimension $n$. In this paper, we study sharp endpoint $L^p$-Sobolev estimates for the solution of the initial value problem for the Schr\"odinger equation, $i \partial_t u + L u=0 $ and show that for all $f\in L^p(X), 1

We study superconductivity in a family of one dimensional incommensurate system with $s$-wave pairing interaction. The incommensurate potential can alter the spatial characteristics of electrons in the normal state, leading to either extended, critical, or localized wave functions. We find that superconductivity is significantly enhanced when the electronic wave function exhibits a critical multifractal structure. This criticality also manifests itself in the power-law dependence of superconducting temperature on the pairing strength. As a consequence, an extended superconducting domain is expected to exist around the localization-delocalization transition, which can be induced by either tuning the amplitude of the incommensurate potential, or by varying the chemical potential across a mobility edge. Our results thus suggest a novel approach to enhance superconducting transition temperature through engineering of incommensurate potential., Comment: 14 pages and 14 figures

The Hardy spaces for Fourier integral operators $\mathcal{H}_{FIO}^{p}(\mathbb{R}^{n})$, for $1\leq p\leq \infty$, were introduced by Smith in [Smith,1998] and Hassell et al. in [Hassell-Portal-Rozendaal,2020]. In this article, we give several equivalent characterizations of $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$, for example in terms of Littlewood--Paley $g$ functions and maximal functions. This answers a question from [Rozendaal,2021]. We also give several applications of the characterizations., Comment: 24 pages. Minor changes to the previous version. To appear in Studia Mathematica

We report a new classical spin liquid in which the collective flux degrees of freedom break the translation symmetry of the honeycomb lattice. This exotic phase exists in frustrated spin-orbit magnets where a dominant off-diagonal exchange, the so-called $\Gamma$ term, results in a macroscopic ground-state degeneracy at the classical level. We demonstrate that the system undergoes a phase transition driven by thermal order-by-disorder at a critical temperature $T_c \approx 0.04 |\Gamma|$. At first sight, this transition reduces an emergent spherical spin-symmetry to a cubic one: spins point predominantly toward the cubic axes at $T < T_c$. However, this seems to simply restore the cubic symmetry of the $\Gamma$ model, and the non-coplanar spins remain disordered below $T_c$. We show that the phase transition actually corresponds to plaquette ordering of hexagonal fluxes and the cubic symmetry is indeed broken, a scenario that is further confirmed by our extensive Monte Carlo simulations., Comment: 7 pages, 6 figures