arXiv 2102.048852021-02-09cond-mat.str-elhep-th

Monopole hierarchy in transitions out of a Dirac spin liquid

Éric Dupuis, William Witczak-Krempa

备注：: 46 pages. Paper submitted to a special issue of Annals of Physics dedicated to Philip W. Anderson
DOI：: 10.1016/j.aop.2021.168496

英文摘要：

Quantum spin liquids host novel emergent excitations, such as monopoles of an emergent gauge field. Here, we study the hierarchy of monopole operators that emerges at quantum critical points (QCPs) between a two-dimensional Dirac spin liquid and various ordered phases. This is described by a confinement transition of quantum electrodynamics in two spatial dimensions (QED3 Gross-Neveu theories). Focusing on a spin ordering transition, we get the scaling dimension of monopoles at leading order in a large-N expansion, where 2N is the number of Dirac fermions, as a function of the monopole's total magnetic spin. Monopoles with a maximal spin have the smallest scaling dimension while monopoles with a vanishing magnetic spin have the largest one, the same as in pure QED3. The organization of monopoles in multiplets of the QCP's symmetry group SU(2) x SU(N) is shown for general N.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

基于瞬子微积分的 Dirac 自旋液体中的单极子及其对称性

Monopoles in Dirac spin liquids and their symmetries from instanton calculus

本文用不依赖共形不变性的半经典瞬子方法，将 DSL 中的单极子构造为 ’t Hooft 顶点，并确定其量子数与二分晶格对称性。

2024-03-10cond-mat.str-elhep-th

模型自旋冰中的磁单极子、狄拉克弦与磁噪声

Monopoles, Dirac strings and Magnetic Noise in Model Spin Ice

本研究基于狄拉克弦形式体系，发现自旋冰哑铃模型与真空中的磁单极子激发具有广泛相似性，重构Stanford实验并模拟磁噪声，证实单极子与约束弦的噪声可分离，长时间关联信号主要源于约束弦。

2025-05-20cond-mat.str-el

Lensing of Dirac monopole in Berry's phase

Berry's phase, which is associated with the slow cyclic motion with a finite period, looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the level crossing point in the parameter space in an exactly solvable model. This topology change of Berry's phase is visualized as a result of lensing effect; the monopole supposed to be located at the level crossing point appears at the displaced point when the variables of the model deviate from the precisely adiabatic movement. The effective magnetic field generated by Berry's phase is determined by a simple geometri…

2021-05-01cond-mat.str-elhep-thnucl-th

A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background

We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge $\pm Q$ separated by a distance $s$ in a periodic $L^3$ lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking $L\to\infty$ at fixed $s/L$. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expecte…

2019-08-14cond-mat.str-elhep-lathep-th

Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in QED3 is lif…

2019-06-13cond-mat.stat-mechcond-mat.str-elhep-th

Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids

Monopole operators are studied in a large family of quantum critical points between Dirac and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED$_{3}$-GN), while for the transitions to Z$_{2}$ QSLs it is a superconducting pairing term with general spin/valley structure (generalized QED$_{…

2022-04-29cond-mat.str-elhep-th

更多相关论文收起更多论文

From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids

The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL) which can be defined on the honeycomb, square, triangular and kagomé lattices. At low energies, the DSL on all these lattices is described by an emergent Quantum Electrodynamics (QED$_3$) with $N_f=4$ flavors of Dirac fermions cou…

2019-04-09cond-mat.str-elhep-lathep-th

大自旋数路线实现稳定的U(1)狄拉克费米子液态于枫叶晶格

Symmetry-resolved monopoles and stability criteria for an $N_f=12$ Dirac spin liquid on the maple-leaf lattice

Massachusetts Institute of Technology（麻省理工学院）；Cornell University（康奈尔大学）；Harvard University（哈佛大学）；Indian Institute of Technology Madras（马德拉斯印度理工学院）

本文通过枫叶晶格实现大自旋数路线，探讨了U(1)狄拉克费米子液态的稳定性问题，发现其具有12个狄拉克费米子，比三角晶格和科赫晶格的4个费米子更多，并通过分类基本单极子来验证其稳定性。

2026-09-10cond-mat.str-el

Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to $SU(4)$ honeycomb models

Dirac spin liquids represent a class of highly-entangled quantum phases in two dimensional Mott insulators, featuring exotic properties such as critical correlation functions and absence of well-defined low energy quasi-particles. Existing numerical works suggest that the spin-orbital $SU(4)$ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice realizes a Dirac spin-orbital liquid, described at low energy by $(2+1)d$ quantum electrodynamics (QED$_3$) with $N_f=8$ Dirac fermions. We generalize methods previously developed for $SU(2)$ spin systems to analyze the symmetry pr…

2021-03-28cond-mat.str-elhep-lathep-th

Dirac-Schwinger 量子化适用于演生磁单极子？

Dirac-Schwinger Quantization for Emergent Magnetic Monopoles?

本文探讨了阻挫自旋冰系统中实验发现的演生磁单极子是否满足 Dirac-Schwinger 电荷量子化条件，并证明在实验误差范围内这些磁荷确实遵守该条件。

2025-04-29cond-mat.str-elhep-ph

刺穿狄拉克自旋液体：从单个单极子到手性态

Piercing the Dirac spin liquid: From a single monopole to chiral states

本文利用变分蒙特卡洛方法研究kagome晶格上狄拉克自旋液体中的规范场效应，构造了无能隙单极子激发并分析了不同规范通量下的手性态。结果表明手性态在最近邻海森堡模型中不稳定，支持无能隙自旋子与单极子共存的物理图像。

2023-11-24cond-mat.str-el

Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7

While sources of magnetic fields - magnetic monopoles - have so far proven elusive as elementary particles, several scenarios have been proposed recently in condensed matter physics of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin ice state is argued to be well-described by networks of aligned dipoles resembling solenoidal tubes - classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defect looks like a magnetic monopole. We demonstrate, by diffuse …

2010-11-04cond-mat.mtrl-scicond-mat.str-el

Dynamics of Dirac strings and monopole-like excitations in chiral magnets under a current drive

Skyrmion lines in metallic chiral magnets carry an emergent magnetic field experienced by the conduction electrons. The inflow and outflow of this field across a closed surface is not necessarily equal, thus it allows for the existence of emergent monopoles. One example is a segment of skyrmion line inside a crystal, where a monopole and antimonopole pair is connected by the emergent magnetic flux line. This is a realization of Dirac string-like excitations. Here we study the dynamics of monopoles in chiral magnets under an electric current. We show that in the process of creation of skyrmion …

2016-02-10cond-mat.mtrl-scicond-mat.str-elnlin.PS

Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification

We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr$^{3+}$ and Tb$^{3+}$, we point out that the inelastic neutron scattering not only detects the low-energy gauge photon, but also contains the continuum of the "magnetic monopole" excitations. Unlike the spinons, these "magnetic monopoles" are purely of quantum origin and have no classical analogue. We further point out that the "magnetic monopole" experiences a background dual "$π$" flux due to the spin-1/2 nature of the local moment when the "monopole" hops on the dual diamond latt…

2017-11-16cond-mat.mtrl-scicond-mat.str-el

Monopole Josephson Effects in a Dirac Spin Liquid

Dirac Spin liquids (DSLs) are gapless featureless states, yet interesting by virtue of the effective field theory describing them -- (2+1)-dimensional quantum electrodynamics (QED$_3$). Further, a DSL is known to be a "parent state" of various seemingly unrelated ordered states, such as antiferromagnets and valence bond solids in the sense that one can obtain ordered states by condensing magnetic monopoles of the emergent gauge field. Can operators in the effective field theory, such as the emergent electric field, be externally induced and measured? In this work, we exploit the parent state p…

2023-03-13cond-mat.mes-hallcond-mat.str-elhep-lat