arXiv subjects

Zijian Xiong

Publications and source records attributed to Zijian Xiong.

14 recordsLinked to original sources

arXiv2026

Constraints from global symmetries of quantum ice on the planar pyrochlore lattice

We study the low energy effective theory of spin-1/2 quantum ice on the planar pyrochlore lattice from the perspective of its global symmetries. We show that the Fourier transform of the spin operator, $S^{z}_{\textbf{Q}}$, can be expressed in terms of conserved quantities associated with a 1-form U(1) symmetry along two high-symmetry momentum paths, leading to constraints on both the static and dynamical structure factors. We also derive Lieb-Schultz-Mattis type constraints that forbid the existence of a unique gapped ground state in the low energy effective theory. Our findings also apply to the (2+1) dimensional U(1) quantum link model.

cond-mat.str-el↗

arXiv2026

Spontaneous continuous-symmetry breaking and tower of states in a comb chain

Based on the study of a one-dimensional (1D) antiferromagnetic Heisenberg model on a comb lattice, this work identifies an example of spontaneous continuous symmetry breaking in a 1D system with short-range interactions. When a symmetry-preserving relevant perturbation is applied to the system, we find that this model can always be described by the Marshall-Lieb-Mattis (MLM) theorem. The Shen-Qiu-Tian theorem establishes a direct connection between the MLM theorem (in the case of bipartite lattices with unequal numbers of sites in the two sublattices) and the breaking of continuous symmetry. Moreover, although authors of previous studies have suggested that the presence of a tower of states (TOS) serves as an important numerical diagnostic of the tendency of a system toward spontaneous symmetry breaking, these investigations have primarily focused on two-dimensional systems. In 1D systems, however, the presence of long-range order does not automatically imply the emergence of a TOS. Here, we observe the existence of a TOS in a 1D realistic ferrimagnetic lattice system with short-range interactions.

cond-mat.str-el↗

arXiv2025

Level spacing statistics of two unitary equivalent models with distinct local symmetries

The full spectrum and integrability of unitary equivalent models are the same. A standard diagnostic tool of integrability is level spacing statistics which requires separating the full spectrum into sectors according to the symmetry. When two unitary equivalent models have different symmetries, it is interesting to know how their level spacing statistics show consistent conclusions. In this work, we examine the level spacing statistics of two unitary equivalent models with distinct local symmetries. The first model is spin-1 XXZ chain $H$, the second model is obtained by Kennedy-Tasaki transformation $U_{KT}HU_{KT}$. We find that the level spacings of model $H$ follow the statistics of the Gaussian orthogonal ensemble (GOE). However, model $U_{KT}HU_{KT}$ only displays GOE statistics in some sectors after a "hidden non-local symmetry" is resolved, and the other sectors labeled by quantum numbers corresponding to the local symmetries exhibit non-GOE statistics. Additionally, a mapping relation between the levels in the sector $\{Z,X,I\}$ of model $H$ and the sector $\{Z,X,I'\}$ of model $U_{KT}HU_{KT}$ is found, where $Z,X,I$ correspond to the quantum numbers of $π$ rotation around $z,x$ axes and bond-centered inversion.

cond-mat.stat-mech↗

arXiv2024

Universal critical dynamics of quantum geometry

In this study, we prove that the quantum critical point in the ground state of quantum many-body systems, can also govern the universal dynamical behavior when the systems are driven far from equilibrium, which can be captured by the evolution of the quantum geometry of the systems. By investigating quantum quench dynamics in quadratic fermionic models, we prove that the quantum volume of these systems typically grows linearly over time, with a growth velocity demonstrating universal behavior: its first derivative over the control parameter exhibits a discontinuity at the quantum critical point, with an universal jump value that is independent of specific models, but is crucially determined by the system dimension. This result reveals universal dynamical properties of non-equilibrium quantum many-body systems

cond-mat.quant-gas↗

arXiv2024

Evidence for distortion-induced local electric polarization in $α$-RuCl$_3$

The spin-orbit assisted Mott insulator $α$-RuCl$_3$ is a prime candidate for material realization of the Kitaev quantum spin liquid. While little attention has been paid to charge degrees of freedom, charge effects, such as electric polarization, may arise in this system. Here, we report distortion-induced local electric polarization in $α$-RuCl$_3$ as evidenced by single-crystal X-ray diffraction, second harmonic generation (SHG) and dielectric measurements. The SHG signal appears at room temperature and develops substantially in the Kitaev paramagnetic state when short-range spin correlations come into play. Despite sizable pyroelectric currents in the Kitaev paramagnetic state, the absence of hysteresis in electric field-dependent polariza-tion (P-E) points to the short-range nature of electric polarization. This localized electric polarization is likely the result of distortion-induced charge dimerization, achieved through virtual hopping-induced charge redistribution. In addition, the electric polarization is boosted by short-range spin correlations via spin-phonon coupling in the Kitaev paramagnetic state. Our results emphasize the importance of charge degrees of freedom in $α$-RuCl$_3$, which establish a novel platform to investi-gate charge effects in Kitaev materials.

cond-mat.str-el↗

arXiv2024

Deconfined quantum phase transition on the kagome lattice: Distinct velocities of spinon and string excitations

Deconfined quantum phase transition (DQPT) provides an extraordinary possibility of the quantum phase transition beyond the Ginzburg-Landau paradigm, which is interwoven with numerous exotic phenomena of the strongly correlated quantum many-body system, e.g. fractional excitation, emergent symmetries, and gauge field. However, various candidates of DQPT have been demonstrated to be weakly first-order, and the conformal field theory (CFT) has to be altered into a non-unitary one. Here we numerically found two linear dispersions with different velocities in one of the few survivors of DQPT -- the extended hard-core Bose-Hubbard model on the Kagome lattice. Such counterintuitive results directly lead to the negation of possible emergent Lorentz symmetry, and the breakdown of conventional theory of DQPT. Furthermore, the snapshots of boson configuration hint that these two velocities may correspond to the dynamics of the fractional excitations and quantum strings, respectively. Our work will inspire the revisit of the theory of DQPT and benefit the field of quantum materials and quantum simulations.

cond-mat.str-el↗

arXiv2023

1-form symmetry and the selection rule of the plaquette valence bond solid phase on kagome lattice

We study the plaquette valence bond solid phase in a XXZ type spin-1/2 model in the kagome lattice. The low energy theory for this phase is a U(1) lattice gauge theory on the honeycomb lattice. We find that there is an emergent 1-form U(1) symmetry in low energy, and there is a mixed anomaly. We also show that this 1-form symmetry constraints the longitudinal dynamical structure factor and leads to the selection rule relating to the vanishing intensity along some high symmetry momentum paths (e.g. $Γ-M$ path). We point out that this emergent 1-form symmetry is robust against the translation symmetry preserving UV perturbation, thus the selection rule will also apply to the model which is obtained by perturbing the classical limit of our model.

cond-mat.str-el↗

arXiv2022

Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model

Gapless edge states are the hallmark of a large class of topological states of matter. Recently, intensive research has been devoted to understanding the physical properties of the edge states at the quantum phase transitions of the bulk topological states. A higher-order symmetry-protected topological state is realized in a plaquette Heisenberg model on the square lattice. In its disordered phase, the lattice with an open boundary hosts either dangling corner states with spin-$1/2$ degeneracy characterizing the topological phase, or nondangling corner states without degeneracy, which depends on the bond configuration near the corners. In this work, we study the critical behavior of these corner states at the quantum critical point (QCP), and find that the spin-$1/2$ corner state induces a new universality class of the corner critical behavior, which is distinct from the ordinary transition of the nondangling corners. In particular, we find that the dangling spin-$1/2$ corner state persists at the QCP despite its coupling to the critical spin fluctuations in the bulk. This shows the robustness of the corner state of the higher-order topological state.

cond-mat.str-el↗

arXiv2022

Fractional and composite excitations of antiferromagnetic quantum spin trimer chains

Using quantum Monte Carlo, exact diagonalization and perturbation theory, we study the spectrum of the $S=1/2$ antiferromagnetic Heisenberg trimer chain by varying the ratio $g=J_2/J_1$ of the intertrimer and intratrimer coupling strengths. The doublet ground states of trimers form effective interacting $S=1/2$ degrees of freedom described by a Heisenberg chain. Therefore, the conventional two-spinon continuum of width $\propto J_1$ when $g=1$ evolves into to a similar continuum of width $\propto J_2$ when $g\to 0$. The intermediate-energy and high-energy modes are termed \emph{doublons} and \emph{quartons} which fractionalize with increasing $g$ to form the conventional spinon continuum. In particular, at $g \approx 0.716$, the gap between the low-energy spinon branch and the high-energy band with mixed doublons, quartons, and spinons closes. These features should be observable in inelastic neutron scattering experiments if a quasi-one-dimensional quantum magnet with the linear trimer structure and $J_2<J_1$ can be identified. Our results may open a window for exploring the high-energy fractional excitations.

cond-mat.str-el↗

arXiv2021

Dynamics in the planar pyrochlore lattice: bow-tie flat band and mixed 't Hooft anomaly

The quantum phase transition between $\mathbb{Z}_{2}$ plaquette valence bound solid (PVBS) and superfluid (SF) phases on the planar pyrochlore lattice (square ice) is under debate, because the conventional deconfined theory does not support continuous one, but the numerical evidence is still not solid. Here, we propose the system can be effectively described by a 2+1 dimensional Abelian-Higgs model which may host the mixed 't Hooft anomaly, so that the deconfinement can exist on the domain walls at the transition point. To verify it, we study the spin excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases, a flat band with bow-tie structure is observed and can be explained by group theoretic analysis. At the transition point, the spectra turn to be continuous and gapless, which indicates the topological excitations. From the snapshot of the spin configuration in real space, we found the existence of the domain wall in which the symmetries satisfy the anomaly. Meanwhile, a Luttinger liquid like continuum implies additional domain walls (point-defect) can emerge in the domain walls (line-defect) and take the role of deconfinement at transition point, as prediction of mixed 't Hooft anomaly. Our work can build a new bridge between the topological gauge field theory and a strongly correlated system.

cond-mat.str-el↗

arXiv2020

Resonant inelastic x-ray scattering study of vector chiral ordered kagome antiferromagnet

We study the resonant inelastic x-ray scattering (RIXS) features of vector chiral ordered kagome antiferromagnets. Utilizing a group theoretical formalism that respects lattice site symmetry, we calculated the $L$ -edge magnon contribution for the vesignieite compound BaCu$_{3}$V$_{2}$O$_{8}$(OH)$_{2}$. We show that polarization dependence of the $L$ -edge RIXS spectrum can be used to track magnon branches. We predict a non-zero $L$ -edge signal in the non-cross $π-π$ polarization channel. At the $K$ -edge, we derived the two-site effective RIXS and Raman scattering operator for two-magnon excitation in vesignieite using the Shastry-Shraiman formalism. Our derivation considers spin-orbit coupling effects in virtual hopping processes. We find vector chiral correlation (four-spin) contribution that is proportional to the RIXS spectrum. Our scattering operator formalism can be applied to a host of non-collinear non-coplanar magnetic materials at both the $L$ and $K$ -edge. We demonstrate that vector chiral correlations can be accessed by RIXS experiments.

cond-mat.str-el↗

arXiv2020

Nonanalyticity of circuit complexity across topological phase transitions

The presence of nonanalyticity in observables is a manifestation of phase transitions. Through the study of two paradigmatic topological models in one and two dimensions, in this work we show that the circuit complexity based on our specific quantification can reveal the occurrence of topological phase transitions, both in and out of equilibrium, by the presence of nonanalyticity. By quenching the system out of equilibrium, we find that the circuit complexity grows linearly or quadratically in the short-time regime if the quench is finished instantaneously or in a finite time, respectively. Notably, we find that for both the sudden quench and the finite-time quench, a topological phase transition in the pre-quench Hamiltonian will be manifested by the presence of nonanalyticity in the first-order or second-order derivative of circuit complexity with respect to time in the short-time regime, and a topological phase transition in the post-quench Hamiltonian will be manifested by the presence of nonanalyticity in the steady value of circuit complexity in the long-time regime. We also show that the increase of dimension does not remove, but only weakens the nonanalyticity of circuit complexity. Our findings can be tested in quantum simulators and cold-atom systems.

cond-mat.str-el↗

arXiv2019

Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure

We study the spin excitation spectra of the two-dimensional spin-$1/2$ Heisenberg model with a checkerboard structures using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions $J_{1}$ and $J_{2}$, and the tuning parameter $g$ is defined as $J_{2}/J_{1}$. The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When $g$ is close to $1$, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the $3\times 3$ checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when $g$ is small. The gapless branch in this case can be regarded as a spin wave in N$\mathrm{\acute{e}}$el order formed by a "block spin" in each $3\times 3$ plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.

cond-mat.str-el↗

arXiv2017

Magnon-phonon coupling effects on the indirect K-edge resonant inelastic X-ray scattering spectrum of a 2D Heisenberg antiferromagnet

We compute the effects of magnon-phonon coupling on the indirect K-edge bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectrum of a square lattice Heisenberg antiferromagnet. We analyze the effects of competing nearest and next--nearest magnetic and magnon-phonon coupling interaction in the RIXS spectrum, for both the antiferromagnetic (AF) and the collinear antiferromagnetic (CAF) phases of the model. Utilizing the Dyson-Maleev representation of spin operators, the Bethe-Salpeter ladder approximation scheme for the bimagnon interacting channel, and considering the lowest order magnon-phonon-magnon scattering interaction we highlight distinct features in the X-ray spectrum. Considering damping effects, arising due to the presence of phonons, we find that in the AF phase the RIXS intensity spectrum attains a maximum value primarily localized around the K $\left(\pm\fracπ{2}, \pm \fracπ{2}\right)$ - point. For the CAF phase the intensity is broadly distributed with a significant scattering intensity located around the Y $\left(\pm\fracπ{2}, 0\right)$ - point. Furthermore, in the CAF phase for suitable anisotropy, nearest-, and next-nearest neighbor interaction parameters the phonon effects can manifest itself as a distinct peak both below and above the bimagnon peak. Such a feature is in contrast to the antiferromagnetic spectrum where the effect due to the phonon peak was located consistently beyond the bimagnon peak in the high energy end of the spectrum. Additionally, in the CAF phase we find the RIXS bimagnon-phonon spectrum to be more sensitive to anisotropy compared to its antiferromagnetic counterpart. We conclude that the ultimate effect of magnon-phonon effects in the indirect K-edge RIXS spectrum, in both the antiferromagnetic and the collinear antiferromagnetic phase, is an observable effect.

cond-mat.str-el↗