arXiv subjects

Ruizhi Liu

Publications and source records attributed to Ruizhi Liu.

12 recordsLinked to original sources

arXiv2026

A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems

In mixed states of quantum systems, symmetries come in two types: strong and weak. Furthermore, it has been argued that in quantum many-body systems, strong symmetries can be "spontaneously broken" down to weak symmetries. An issue is that as previously formulated, such "strong-to-weak symmetry breaking" appears to be a fairly non-local effect. In this paper, we show how to understand and diagnose strong symmetries and strong-to-weak symmetry breaking in an explicitly local way. Our main technical tool is a rigorous definition of strong symmetry in the limit of infinite volume, which generalizes the conventional finite-volume definitions, and for which we give several equivalent formulations, including one involving the concept of "local charge coherence". Finally, we introduce von Neumann systems, which in infinite-volume symmetries are intermediate between strong and weak symmetries. We derive a Lieb-Schultz-Mattis type anomaly constraint for von Neumann symmetries (and therefore, in particular, strong symmetries) in quantum spin chains.

quant-ph↗

arXiv2026

Anomalies in quantum spin systems and Nielsen-Ninomiya type Theorems

We provide an algebraic perspective on Nielsen--Ninomiya-type no-go theorems arising from group cohomological anomalies, revisiting in particular the version proved by Kapustin and Sopenko. Departing from their analytic proof, our approach emphasizes the algebraic structure of symmetry actions and the local computability of anomaly indices. We demonstrate that this no-go theorem is due to a fundamental algebraic incompatibility between anomaly data and the dimension of local Hilbert spaces. Specifically, when an anomaly index is locally computable via quasi-local unitary operators, a suitable gauge fixing trivializes their (generalized) determinants, imposing unexpected and nontrivial constraints on lattice regularizations.

math-ph↗

arXiv2026

When does a lattice higher-form symmetry flow to a topological higher-form symmetry at low energies?

We study the lattice version of higher-form symmetries on tensor-product Hilbert spaces. Interestingly, at low energies, these symmetries may not flow to the topological higher-form symmetries familiar from relativistic quantum field theories, but instead to non-topological higher-form symmetries. We present concrete lattice models exhibiting this phenomenon. One particular model is an $\mathbb{R}$ generalization of the Kitaev honeycomb model featuring an $\mathbb{R}$ lattice 1-form symmetry. We show that its low-energy effective field theory is a gapless, non-relativistic theory with a non-topological $\mathbb{R}$ 1-form symmetry. In both the lattice model and the effective field theory, we demonstrate that the non-topological $\mathbb{R}$ 1-form symmetry is not robust against local perturbations. In contrast, we also study various modifications of the toric code and their low-energy effective field theories to demonstrate that the compact $\mathbb{Z}_2$ lattice 1-form symmetry does become topological at low energies unless the Hamiltonian is fine-tuned. Along the way, we clarify the rules for constructing low-energy effective field theories in the presence of multiple superselection sectors. Finally, we argue on general grounds that non-compact higher-form symmetries (such as $\mathbb{R}$ and $\mathbb{Z}$ 1-form symmetries) in lattice systems generically remain non-topological at low energies, whereas compact higher-form symmetries (such as $\mathbb{Z}_{n}$ and $U(1)$ 1-form symmetries) generically become topological.

cond-mat.str-el↗

arXiv2026

Designing faster mixed integer linear programming algorithm via learning the optimal path

Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations. Solving these problems typically employs the branch-and-bound algorithm, the core of which can be conceived as searching for a path of nodes (or sub-problems) that contains the optimal solution to the original MILP problem. Traditional approaches to finding this path rely heavily on hand-crafted, intuition-based heuristic strategies, which often suffer from unstable and unpredictable performance across different MILP problem instances. To address this limitation, we introduce DeepBound, a deep learning-based node selection algorithm that automates the learning of such human intuition from data. The core of DeepBound lies in learning to prioritize nodes containing the optimal solution, thereby improving solving efficiency. DeepBound introduces a multi-level feature fusion network to capture the node representations. To tackle the inherent node imbalance in branch-and-bound trees, DeepBound employs a pairwise training paradigm that enhances the model's ability to discriminate between nodes. Extensive experiments on three NP-hard MILP benchmarks demonstrate that DeepBound achieves superior solving efficiency over conventional heuristic rules and existing learning-based approaches, obtaining optimal feasible solutions with significantly reduced computation time. Moreover, DeepBound demonstrates strong generalization capability on large and complex instances. The analysis of its learned features reveals that the method can automatically discover more flexible and robust feature selection, which may effectively improve and potentially replace human-designed heuristic rules.

cs.AI↗

arXiv2025

Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement

We establish multiple interrelated, fundamental results in quantum many-body systems that can have long-range interactions. For a sufficiently long quantum spin chain, we first show that if the multi-spin interactions in the Hamiltonian decay fast enough as their ranges increase and the Hamiltonian is gapped, then the ground states satisfy the entanglement area law, even if there is a ground state degeneracy due to a spontaneously broken discrete symmetry. This area law also holds for certain excited states. Second, if such a long-range interacting Hamiltonian has an anomalous symmetry, then the Lieb-Schultz-Mattis theorem applies, i.e., the Hamiltonian cannot have a unique gapped symmetric ground state. If the Hamiltonian contains only 2-spin interactions, these results hold when the interactions decay faster than $1/r^2$, with $r$ the distance between the two interacting spins. Third, we show that pure states with an anomalous symmetry, which may not be a ground state of any natural Hamiltonian, must be long-range entangled. The symmetries we consider include on-site internal symmetries combined with lattice translation symmetries, and they can also extend to purely internal but non-on-site symmetries. Moreover, these internal symmetries can be discrete or continuous. We explore the applications of these results through various examples.

cond-mat.str-el↗

arXiv2025

Twisted locality-preserving automorphisms, anomaly index, and generalized Lieb-Schultz-Mattis theorems with anti-unitary symmetries

Symmetries and their anomalies are powerful tools to understand quantum matter. In this work, for quantum spin chains, we define twisted locality-preserving automorphisms and their Gross-Nesme-Vogts-Werner indices, which provide a unified framework to describe both unitary and anti-unitary symmetries, on-site and non-on-site symmetries, and internal and translation symmetries. For a symmetry $G$ with actions given by twisted locality-preserving automorphisms, we give a microscopic definition of its anomaly index, which is an element in $H^3_φ(G; U(1))$, where the subscript $φ$ means that anti-unitary elements of $G$ act on $U(1)$ by complex conjugation. We show that an anomalous symmetry leads to multiple Lieb-Schultz-Matttis-type theorems. In particular, any state with an anomalous symmetry must either have long-range correlation or violate the entanglement area law. Based on this theorem, we further deduce that any state with an anomalous symmetry must have long-range entanglement, and any Hamiltonian that has an anomalous symmetry cannot have a unique gapped symmetric ground state, as long as the interactions in the Hamiltonian decay fast enough as the range of the interaction increases. For Hamiltonians with only two-spin interactions, the last theorem holds if the interactions decay faster than $1/r^2$, where $r$ is the distance between the two interacting spins. We demonstrate these general theorems in various concrete examples.

cond-mat.str-el↗

arXiv2025

Lovász Meets Lieb-Schultz-Mattis: Complexity in Approximate Quantum Error Correction

Approximate quantum error correction (AQEC) provides a versatile framework for both quantum information processing and probing many-body entanglement. We reveal a fundamental tension between the error-correcting power of an AQEC and the hardness of code state preparation. More precisely, through a novel application of the Lovász local lemma, we establish a fundamental trade-off between local indistinguishability and circuit complexity, showing that orthogonal short-range entangled states must be distinguishable via a local operator. These results offer a powerful tool for exploring quantum circuit complexity across diverse settings. As applications, we derive stronger constraints on the complexity of AQEC codes with transversal logical gates and establish strong complexity lower bounds for W state preparation. Our framework also provides a novel perspective for systems with Lieb-Schultz-Mattis type constraints.

quant-ph↗

arXiv2025

On whether quantum theory needs complex numbers: the foil theories perspective

Recent work by Renou et al. (2021) has led to some controversy concerning the question of whether quantum theory requires complex numbers for its formulation. We promote the view that the main result of that work is best understood not as a claim about the relative merits of different representations of quantum theory, but rather as a claim about the possibility of experimentally adjudicating between standard quantum theory and an alternative theory -- a foil theory -- known as real-amplitude quantum theory (RQT). In particular, the claim is that this adjudication can be achieved given only an assumption about the causal structure of the experiment. Here, we aim to shed some light on why this is possible, by reconceptualizing the comparison of the two theories as an instance of a broader class of such theory comparisons. By recasting RQT as the subtheory of quantum theory that arises by symmetrizing with respect to the collective action of a time-reversal symmetry, we can compare it to other subtheories that arise by symmetrization, but for different symmetries. If the symmetry has a unitary representation, the resulting foil theory is termed a twirled quantum world, and if it does not (as is the case in RQT), the resulting foil theory is termed a swirled quantum world. We show that, in contrast to RQT, there is no possibility of distinguishing any twirled quantum world from quantum theory given only an assumption about causal structure. We also define analogues of twirling and swirling for an arbitrary generalized probabilistic theory and identify certain necessary conditions on a causal structure for it to be able to support a causal compatibility gap between the theory and its symmetrized version. We draw out the implications of these analyses for the question of how a lack of a shared reference frame state features into the possibility of such a gap.

quant-ph↗

arXiv2025

Higher obstructions to conformal boundary conditions and lattice realizations

Although it is long believed that vanishing of chiral central charges of a 2d conformal field theory (CFT) implies the existence of conformal boundary conditions, there are yet higher obstructions. In this paper, we focus on 2d rational CFTs, for which we identify a series of obstructions, known as higher central charges. We also discuss its implication for lattice realizations and the generalization with global symmetries.

hep-th↗

arXiv2024

Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries

Higher-matter is defined by higher-representation of a symmetry algebra, such as the $p$-form symmetries, higher-group symmetries or higher-categorical symmetries. In this paper, we focus on the cases of higher-group symmetries, which are formulated in terms of the strictification of weak higher-groups. We systematically investigate higher-matter charged under 2-group symmetries, defined by automorphism 2-representations. Furthermore, we construct a Lagrangian formulation of such higher-matter fields coupled to 2-group gauge fields in the path space of the spacetime manifold. We interpret such model as the Landau-Ginzburg theory for 2-group symmetries, and discuss the spontaneous symmetry breaking (SSB) of 2-group symmetries under this framework. Examples of discrete and continuous 2-groups are discussed. Interestingly, we find that a non-split 2-group symmetry can admit an SSB to a split 2-group symmetry, where the Postnikov class is trivialized. We also briefly discuss the strictification of weak 3-groups, weak 3-group gauge fields and 3-representations in special cases.

hep-th↗

arXiv2024

Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter

We analyze the internal symmetries and their anomalies in the Kitaev spin-$S$ models. Importantly, these models have a lattice version of a $\mathbb{Z}_2$ 1-form symmetry, denoted by $\mathbb{Z}_2^{[1]}$. There is also an ordinary 0-form $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T$ symmetry, where $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}$ are $π$ spin rotations around two orthogonal axes, and $\mathbb{Z}_2^T$ is the time reversal symmetry. The anomalies associated with the full $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T\times\mathbb{Z}_2^{[1]}$ symmetry are classified by $\mathbb{Z}_2^{17}$. We find that for $S\in\mathbb{Z}$ the model is anomaly-free, while for $S\in\mathbb{Z}+\frac{1}{2}$ there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these symmetries and anomalies apply to not only the Kitaev spin-$S$ models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, generically these consequences still apply even if the perturbations break the 1-form symmetry. A notable consequence is that there should generically be a deconfined fermionic excitation carrying no fractional quantum number under the $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T$ symmetry if $S\in\mathbb{Z}+\frac{1}{2}$, which implies symmetry-enforced exotic quantum matter. We also discuss the consequences for $S\in\mathbb{Z}$.

cond-mat.str-el↗

arXiv2023

iEDA: An Open-Source Intelligent Physical Implementation Toolkit and Library

Open-source EDA shows promising potential in unleashing EDA innovation and lowering the cost of chip design. This paper presents an open-source EDA project, iEDA, aiming for building a basic infrastructure for EDA technology evolution and closing the industrial-academic gap in the EDA area. iEDA now covers the whole flow of physical design (including Floorplan, Placement, CTS, Routing, Timing Optimization etc.), and part of the analysis tools (Static Timing Analysis and Power Analysis). To demonstrate the effectiveness of iEDA, we implement and tape out three chips of different scales (from 700k to 1.5M gates) on different process nodes (110nm and 28nm) with iEDA. iEDA is publicly available from the project home page http://ieda.oscc.cc.

cs.AR↗