arXiv subjects

Kangle Li

Publications and source records attributed to Kangle Li.

12 recordsLinked to original sources

arXiv2026

Local observable errors from truncating interaction tails in gapped quantum lattice systems

We bound the error in ground-state expectations of local observables caused by truncating the spatial tails of a gapped quantum lattice Hamiltonian. We show that the error is controlled by the interaction strength discarded near each site, rather than by the extensive norm of the omitted Hamiltonian. If the gap remains open along a path that removes the interaction tail, the resulting bounds are uniform in system size and extend, under suitable assumptions, to thermodynamic-limit ground states. The convergence rate reflects the decay of the interaction tail: it is algebraic for power-law interactions, superpolynomial for superpolynomial interactions, and exponential at any strictly smaller rate for exponentially decaying interactions. For superpolynomial interactions, we also derive a direct infinite-volume estimate using automorphic equivalence. The results extend to isolated low-energy sectors and parity-even fermionic systems. For two-body interactions decaying as $r^{-p}$ in $d$ dimensions, we prove an error bound $O(R^{-(p-d)})$ for $p>2d$, where $R$ is the truncation range. We construct a gapped non-translation-invariant example that saturates this scaling, showing that the bound is optimal for the general class considered. Our results quantify when finite-range truncations faithfully reproduce the local physics of gapped long-range systems.

quant-ph↗

arXiv2026

Topological phases and quantum criticality from $SU(2)$ Chern-Simons-matter theories

Motivated by recent numerical studies where various $SU(2)$ Chern-Simons-matter theories emerge, we analytically study topological phases and quantum criticality in two-dimensional systems described by such theories. First, we classify $SU(2)_k$ topological orders in all lattice spin systems with a $p4\times SO(3)$ symmetry, where $k$ is an arbitrary nonzero integer. We find that for each odd $k$, the topological order can emerge in systems with an arbitrary Lieb-Schultz-Mattis (LSM) anomaly, and the symmetry cannot permute anyons. If the system has a nontrivial (respectively, trivial) LSM anomaly, then there is exactly one (respectively, nine) symmetry-enriched topological (SET) phases. On the other hand, $SU(2)_k$ topological order with any even $k$ can only emerge in systems with a trivial LSM anomaly. If $k\notin\{6, 10, 14, \cdots\}$, the symmetry cannot permute anyons, and there are 16 SET phases. If $k\in\{6, 10, 14, \cdots\}$, there are 4 different ways how the symmetry can permute anyons, and there are 64 SET phases. Next, we analyze the $SU(2)_k$ Chern-Simons theories coupled to $N_f$ flavors of gapless matter fields that can be either bosonic or fermionic. For both types of theories, we consider a joint large-$N_f$ and large-$k$ limit with $N_f/k$ fixed, and compute the scaling dimensions of the bilinear operators of the bosons or fermions to the order of $1/N_f$. These results sharpen our understanding of these emergent exotic topological phases and quantum criticality, and provide useful guidance to explore them further.

cond-mat.str-el↗

arXiv2026

Beyond Global Similarity: Towards Fine-Grained, Multi-Condition Multimodal Retrieval

Recent advances in multimodal large language models (MLLMs) have substantially expanded the capabilities of multimodal retrieval, enabling systems to align and retrieve information across visual and textual modalities. Yet, existing benchmarks largely focus on coarse-grained or single-condition alignment, overlooking real-world scenarios where user queries specify multiple interdependent constraints across modalities. To bridge this gap, we introduce MCMR (Multi-Conditional Multimodal Retrieval): a large-scale benchmark designed to evaluate fine-grained, multi-condition cross-modal retrieval under natural-language queries. MCMR spans five product domains: upper and bottom clothing, jewelry, shoes, and furniture. It also preserves rich long-form metadata essential for compositional matching. Each query integrates complementary visual and textual attributes, requiring models to jointly satisfy all specified conditions for relevance. We benchmark a diverse suite of MLLM-based multimodal retrievers and vision-language rerankers to assess their condition-aware reasoning abilities. Experimental results reveal: (i) distinct modality asymmetries across models; (ii) visual cues dominate early-rank precision, while textual metadata stabilizes long-tail ordering; and (iii) MLLM-based pointwise rerankers markedly improve fine-grained matching by explicitly verifying query-candidate consistency. Overall, MCMR establishes a challenging and diagnostic benchmark for advancing multimodal retrieval toward compositional, constraint-aware, and interpretable understanding. Our code and dataset is available at https://github.com/EIT-NLP/MCMR

cs.CV↗

arXiv2025

Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter

For spin and fermionic systems in any spatial dimension, we establish that the superpolynomial decay behavior of mutual information and conditional mutual information is a universal property of gapped pure- and mixed-state phases; i.e., all systems in such a phase possess this property if one system in this phase possesses this property. We further demonstrate that the (conditional) mutual information indeed decays superpolynomially in a large class of phases, including chiral phases. As a by-product, we sharpen the notion of mixed-state phases.

cond-mat.str-el↗

arXiv2025

Stabilizer Perturbation Theory: A Systematic Construction via Schrieffer-Wolff Transformation

Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have gained increasing prominence as another class of models for quantum systems thanks to the recent advances in experimentally realizing mesoscopic quantum devices. Stabilizer states, innately defined on systems of qudits, have correspondingly emerged as another class of classically simulatable starting point for the study of quantum error-correcting codes and topological phases of matter in such devices. As a step towards analyzing more general quantum many-body problems on these platforms, we develop a systematic stabilizer perturbation theory in qubit systems. Our approach relies on the local Schrieffer-Wolff transformation, which we show can be efficiently performed through the binary encoding the Pauli algebra. As demonstrations, we first benchmark the stabilizer perturbation theory on the transverse field Ising chain in one dimension. The method is then further applied to $\mathbb{Z}_2$ toric code on square lattice and kagome lattice to probe the tendency toward confinement for anyonic excitations.

quant-ph↗

arXiv2024

Symmetry-enforced minimal entanglement and correlation in quantum spin chains

The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the $SO(3)$ spin rotation symmetry and lattice translation symmetry in a quantum spin-$J$ chain, with $J$ a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal R\'enyi-$\alpha$ entropy compatible with these symmetries is $\min\{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) \}$, for any $\alpha\in\mathbb{R}^+$. In an infinitely long open chain with such symmetries, for any $\alpha\in\mathbb{R}^+$ the minimal R\'enyi-$\alpha$ entropy of half of the system is $\min\{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) \}$. When $\alpha\rightarrow 1$, these lower bounds give the symmetry-enforced minimal von Neumann entropies in these setups. Moreover, we show that no state in a quantum spin-$J$ chain with these symmetries can have a vanishing correlation length. Interestingly, the states with the minimal entanglement may not be a state with the minimal correlation length.

cond-mat.str-el↗

arXiv2024

Quantum metric driven transition between superfluid and incoherent fluid

We study the interplay between repulsive interaction and superfluidity in flat band system. We consider spatially indirect excitons in the Lieb lattice bilayer as an example. We show that due to the presence of repulsive interaction, the excitons may form an incoherent fluid. By increasing the quantum metric, the exciton fluid experiences a transition into the superfluid phase. Such transition may be captured by a model of Josephson junction array, which is beyond mean field description.

cond-mat.str-el↗

arXiv2024

Constructive Fermionic Matrix Product States for Projected Fermi Sea

Projected wave functions offer a means for incorporating local correlation effects in gapless electronic phases of matter like metals. Although such wave functions can be readily specified formally, it is challenging to compute their associated physical observables. Tensor network approaches offer a modern numerical method for this task. In this work, we develop and demonstrate a constructive tensor-network approach for obtaining physical quantities, like fermion two-point functions and density-density correlation functions, for one-dimensional projected Fermi sea states. We benchmark our method against exact analytical results for spin-1/2 electrons subjected to the Gutzwiller projection, and then present results on spinless fermions with nearest-neighbor repulsion. For a state with two pairs of Fermi points, we reveal a correlation-tuning of the characteristic wave vector of the charge density modulation in the system.

cond-mat.str-el↗

arXiv2023

Stacked tree construction for free-fermion projected entangled pair states

The tensor network representation of a state in higher dimensions, say a projected entangled-pair state (PEPS), is typically obtained indirectly through variational optimization or imaginary-time Hamiltonian evolution. Here, we propose a divide-and-conquer approach to directly construct a PEPS representation for free-fermion states admitting descriptions in terms of filling exponentially localized Wannier functions. Our approach relies on first obtaining a tree tensor network description of the state in local subregions. Next, a stacking procedure is used to combine the local trees into a PEPS. Lastly, the local tensors are compressed to obtain a more efficient description. We demonstrate our construction for states in one and two dimensions, including the ground state of an obstructed atomic insulator on the square lattice.

cond-mat.str-el↗

arXiv2021

Quantum Steering Ellipsoid and Unruh Effect

Quantum steering is a perplexing feature at the heart of quantum mechanics that provides profound implications in understanding the nature of physical reality. On the other hand, the effect of relativistic features on quantum systems is vital in understanding the underlying foundations of physics. In this work, we study the effects of Unruh acceleration on the quantum steering of a two-qubit system. In particular, we consider the so-called quantum steering ellipsoid and the maximally-steered coherence in a non-inertial frame and find closed-form analytic expressions for the role of the Unruh acceleration in these quantities. Analyzing the conditions for the steerability of the system, we develop a geometric description for the effect of Unruh acceleration on the quantum steering of a two-qubit system.

quant-ph↗

arXiv2021

Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions

We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest. The correspondence between fermionic and bosonic operators is established with the help of auxiliary Majorana fermions. The current construction is applicable to general lattices with even coordination number and an arbitrary number of fermion flavors. The approach is demonstrated on the single-orbital square, triangular and cubic lattices for spin-1/2 fermions. We also discuss the relation to some quantum spin liquid models.

cond-mat.str-el↗

arXiv2017

Searching for the Subatomic Swirls in the CuCu and CuAu Collisions

Recently the STAR Collaboration discovered the "subatomic swirls", that is, the most vortical fluid flow structures in the quark-gluon plasma produced via the AuAu collisions at the Relativistic Heavy Ion Collider (RHIC). Published in Nature and featured as a cover story, this discovery attracted significant interest and generated wide enthusiasm. For such an important finding, it is crucial to look for independent evidences of confirmation and to critically test the current interpretation of the global polarization measurement. We suggest that the CuCu and CuAu colliding systems at RHIC provide such opportunity. Interestingly, our calculations reveal that the fluid vorticity in the CuCu or CuAu collision is comparable to that in the AuAu Collision. Surprisingly, we find the computed $\Lambda$ hyperon polarization effect is stronger in the CuCu and CuAu systems than the AuAu system at the same collisional beam energy and centrality class, with an interesting hierarchy CuCu $>$ CuAu $>$ AuAu due to interplay between $\Lambda$ production timing and the time evolution of the vorticity. These predictions can be readily tested by experimental data.

nucl-th↗