arXiv subjects

Jinmin Yi

Publications and source records attributed to Jinmin Yi.

13 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

Order-disorder trade-off in dirty quantum systems

We prove a trade-off theorem for order and disorder parameters in one-dimensional quantum spin systems with quenched disorder. For a disordered ensemble with exact Ising symmetry and average translation symmetry, any gapped ensemble must have one and only one of the following: an $O(1)$ order parameter or an $O(1)$ disorder parameter with even parity, both of the Edwards-Anderson type. The result extends to nearly gapped ensembles that accommodate Griffiths-type rare-region effects. These results offer a powerful and rigorous framework to understand the disorder effects beyond perturbative approaches. As applications, we (1) establish the existence of string order parameters for SPT phases; (2) derive a Lieb-Schultz-Mattis-type constraint for disordered ensembles, which requires a nearly gapped ensemble to spontaneously break the symmetry; and (3) discuss similar trade-off relations for disordered fermion chains, leading to an improved understanding of certain "intrinsically disordered" topological phases.

cond-mat.dis-nn↗

arXiv2026

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

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

Entanglement sharing schemes

We ask how quantum correlations can be distributed among many subsystems. To address this, we define entanglement sharing schemes (ESS) where certain pairs of subsystems allow entanglement to be recovered via local operations, while other pairs must not. ESS schemes come in two variants, one where the partner system with which entanglement should be prepared is known, and one where it is not. In the case of known partners, we fully characterize the access structures realizable for ESS when using stabilizer states, and construct efficient schemes for threshold access structures, and give a conjecture for the access structures realizable with general states. In the unknown partner case, we again give a complete characterization in the stabilizer setting, additionally give a complete characterization of the case where there are no restrictions on unauthorized pairs, and we prove a set of necessary conditions on general schemes which we conjecture are also sufficient. Finally, we give an application of the theory of entanglement sharing to resolve an open problem related to the distribution of entanglement in response to time-sensitive requests in quantum networks.

quant-ph↗

arXiv2025

Disordered Weyl semimetal as an array of coupled Hubbard chains

We demonstrate that a disordered magnetic Weyl semimetal may be mapped onto a two-dimensional array of coupled replicated Hubbard chains, where the Hubbard $U$ is directly related to the variance of the disorder potential. This is a three-dimensional generalization of a similar mapping of the two-dimensional quantum Hall plateau transition to a one-dimensional Hubbard chain. We demonstrate that this mapping leads to the conclusion that the Weyl semimetal becomes a diffusive metal with a nonzero density of states at arbitrarily weak disorder, in agreement with recent work. We also discuss the absence of localization in strongly disordered Weyl semimetals from the viewpoint of this mapping.

cond-mat.mes-hall↗

arXiv2025

Noise-strength-adapted approximate quantum codes inspired by machine learning

We demonstrate that machine learning provides a powerful tool for discovering new approximate quantum error-correcting (AQEC) codes beyond conventional algebraic frameworks. Building upon direct observations through hybrid quantum-classical learning, we discover two new 4-qubit amplitude damping codes with an innovative noise-strength-adaptive (NSA) feature where the codeword varies with noise strength. They are NSA self-complementary and NSA pair-complementary codes. We show that they can both outperform conventional codes for amplitude damping (AD) noise. The 4-qubit self-complementary NSA code outperforms the standard LNCY AD code in fidelity and Knill-Laflamme condition violation. The pair-complementary code, which has no known non-NSA analog, achieves even better performance with higher-order loss suppression and better fidelity. We further generalize both approaches to families of NSA AD codes for arbitrary system size, as well as an NSA variant of the 0-2-4 binomial code for single-photon loss. Our results demonstrate that adaptation to noise strength can systematically lead to significant improvements in error correction capability, and also showcase how machine learning can help discover new valuable code formalisms that may not emerge from traditional design approaches.

quant-ph↗

arXiv2024

Complexity and order in approximate quantum error-correcting codes

We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems, covering systems with both all-to-all connectivity and geometric scenarios like lattice systems in finite spatial dimensions. To this end, we introduce a type of code parameter that we call subsystem variance, which is closely related to the optimal AQEC precision. Our key finding is that, for a code encoding $k$ logical qubits in $n$ physical qubits, if the subsystem variance is below an $O(k/n)$ threshold, then any state in the code subspace must obey certain circuit complexity lower bounds, which identify nontrivial "phases" of codes. Based on our results, we propose $O(k/n)$ as a boundary between subspaces that should and should not count as AQEC codes. This theory of AQEC provides a versatile framework for understanding quantum complexity and order in many-body quantum systems, generating new insights for wide-ranging physical scenarios, in particular topological order and critical quantum systems which are of outstanding importance in many-body and high energy physics. We observe from various different perspectives that roughly $O(1/n)$ represents a common, physically significant "scaling threshold" of subsystem variance for features associated with nontrivial quantum order.

quant-ph↗

arXiv2024

Absence of localization in Weyl semimetals

One of the fundamental facts of condensed matter physics is that sufficient amount of disorder always turns a Fermi liquid metal into an Anderson insulator: a compressible, but non-conducting phase of matter. Recently, topological semimetals have emerged as another way a metallic phase may be realized. In this paper we point out that, unlike ordinary metals, at least some topological semimetals are immune to localization, provided certain conditions are satisfied. We present several physical arguments, based on diagrammatic perturbation theory and Keldysh field theory, as well as domain wall network construction, to back up this claim.

cond-mat.mes-hall↗

arXiv2023

Topological order in interacting semimetals

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a nonabelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED$_3$ to $3+1$ dimensions. In addition we discuss a $(3+1)$-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

cond-mat.str-el↗

arXiv2018

Deep Learning Topological Invariants of Band Insulators

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.

cond-mat.str-el↗