I give a pedagogical introduction to some of the many particles and gauge fields that can emerge in correlated matter. The standard model of materials is built on Landau's foundational principles: adiabatic continuity and spontaneous symmetry breaking. These ideas lead to quasiparticles that inherit their quantum numbers from fundamental particles, Nambu-Goldstone bosons, the Anderson-Higgs mechanism, and topological defects in order parameters. I then describe the modern discovery of physics beyond the standard model. Here, quantum correlations (entanglement) and topology play key roles in defining the properties of matter. This can lead to fractionalised quasiparticles that carry only a fraction of the quantum numbers that define fundamental particles. These particles can have exotic properties: for example Majorana fermions are their own antiparticles, anyons have exchange statistics that are neither bosonic nor fermionic, and magnetic monopoles do not occur in the vacuum. Gauge fields emerge naturally in the description of highly correlated matter and can lead to gauge bosons. Relationships to the standard model of particle physics are discussed.
The Chamon model is an exactly solvable spin Hamiltonian exhibiting nontrivial fracton order. In this work, we dissect two distinct aspects of the model. First, we show that it exhibits an emergent fractonic gauge theory coupled to a fermionic subsystem symmetry-protected topological state under four stacks of $\mathbb{Z}_2$ planar symmetries. Second, we show that the Chamon model hosts 4-foliated fracton order by describing an entanglement renormalization group transformation that exfoliates four separate stacks of 2D toric codes from the bulk system.
Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations. Here we experimentally investigate the emergent $\mathbb{Z}_2$ gauge invariance in a 1D superconducting circuit with 10 transmon qubits. By precisely adjusting staggered longitudinal and transverse fields to each qubit, we construct an effective Hamiltonian containing an LGT and gauge-broken terms. The corresponding matter sector can exhibit a localization, and there also exists a 3-qubit operator, of which the expectati…
Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent $\mathbb{Z}_2$ gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological $\mathbb{Z}_2$ quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also …
We consider spontaneous symmetry breaking transitions of strongly interacting two-dimensional Dirac fermions minimally coupled to mass and emergent gauge field order parameters. Using a renormalization group analysis, we show that the presence of gauge fields leads to novel fermion induced quantum (multi-)criticality where the putative emergent Lorentz invariance is violated. We illustrate this with the example of translational symmetry breaking due to charge-density wave order on the honeycomb lattice. Finally, we identify that topological phase transitions are well described by this effectiv…
Emergent superconformal symmetry in the phase diagram of a 1D $\mathbb{Z}_{2}$ lattice gauge theory
Karlstad University（卡尔斯特大学）；Andronikashvili Institute of Physics（安德罗尼卡什维利物理研究所）；Ilia State University（伊利亚州立大学）；Heinrich-Heine-Universität（海因里希·海涅大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging planar or fractal subsystem fermion parity symmetry in three spatial dimensions gives rise to a plethora of exactly solvable spin models exhibiting novel gapped fractonic orders characterized by emergent fermionic gauge theory. The low energy excitations of these models include fractional quasiparticles with constrained mobility and emergent fermionic statisti…
We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in t…
We present a realization of fracton-elasticity duality purely formulated in terms of ordinary gauge fields, encompassing standard elasticity and incommensurate crystals as those describing twisted bilayer graphene, quasicrystals or more general moiré lattices. Our construction comprises a description of all types of two-dimensional defects: disclinations, dislocations, discompressions and point-like defects, and takes into account body forces and impurities. The original form of the duality in terms of tensor gauge fields is recovered after partial gauge fixing. We identify the coupling of eac…
We address emergent higher-form symmetry in Higgs phases with superfluidity. The emergent symmetry appears if a matter field is invariant under a transformation of a common subgroup of gauge and global $\mathrm{U}(1)$ symmetries. We explicitly construct the symmetry generator that is topological and gauge invariant in a low-energy effective theory. Such emergent symmetry is helpful to distinguish the Higgs and other phases with superfluidity, such as phases of QCD at finite density. We also discuss the possibility of phase transition between these phases.
We investigate the interplay of quantum one-dimensional discrete $\mathbb{Z}_2$ gauge fields and fermion matter near full filling in terms of deconfined fractionalized hole excitations that constitute mobile domain walls between vacua that break spontaneously translation symmetry. In the limit of strong string tension, we uncover emergent integrable correlated hopping dynamics of holes which is complementary to the constrained XXZ description in terms of bosonic dimers. We analyze numerically quantum dynamics of spreading of an isolated hole together with the associated time evolution of entan…
Kondo effect is a prominent quantum phenomenon describing the many-body screening of a local magnetic impurity. Here, we reveal a new type of non-magnetic Kondo behavior generated by gauge fluctuations in strongly-correlated baths. We show that a non-magnetic bond defect not only introduces the potential scattering but also locally enhances the gauge fluctuations. The local gauge fluctuations further mediate a pseudospin exchange interaction that produces an asymmetric Kondo fixed point in low-energy. The gauge-fluctuation-induced Kondo phenomena do not exhibit the characteristic resistivity b…
Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors. Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation-invariant. In a recent work [Halimeh, Zhao, Hauke, and Knolle, arXiv:2111.02427], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in $\mathrm{U}(1)$ gauge theories against gauge erro…
We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension $D=3$; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsio…
We revisit the theory of strongly correlated quantum matter perturbed by Harris-marginal random-field disorder, using the simplest holographic model. We argue that for weak disorder, the ground state of the theory is not Lifshitz invariant with a non-trivial disorder-dependent dynamical exponent, as previously found. Instead, below a non-perturbatively small energy scale, we predict infrared physics becomes independent of the disorder strength.
The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries naturally (unless we engineer fine-tuned toy models to realize higher symmetries). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that spontaneously broken emergent higher symmetries are nothing but a kind of topological orders. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possi…
Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the $U(1)$ fracton models. We study some of the phases …
We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory, that was recently shown in Monte Carlo simulations to exhibit $\mathbb{Z}_2$ topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with co-incident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well understood in terms of condensing magn…
Emergent gauge flux in mixed QED$_3$ with flavor chemical potential: application to magnetized U(1) Dirac spin liquids
The University of Hong Kong（香港大学）；HK Institute of Quantum Science & Technology（香港量子科学院）；State Key Laboratory of Optical Quantum Materials（光学量子材料国家重点实验室）；University of Cologne（科隆大学）；University of Utah（犹他大学）；Kavli Institute for Theoretical Physics（卡弗里理论物理研究所）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；French American Center for Theoretical Science（法美理论科学中心）；CNRS（法国国家科学研究中心）；KITP（卡弗里理论物理研究所）；Canadian Institute for Advanced Research（加拿大高级研究院）
We consider the Abelian Higgs model in 3+1 dimensions with vortex lines, into which charged fermions are introduced. This could be viewed as a model of a type-II superconductor with unpaired electrons (or holes), analogous to the boson-fermion model of high-$T_c$ superconductors but one in which the bosons and fermions interact only through the electromagnetic gauge field. We investigate the dual formulation of this model, which is in terms of a massive antisymmetric tensor gauge field $B_{μν}$ mediating the interaction of the vortex lines. This field couples to the fermions through a nonlocal…
We study the origin of Lorentz force on the spinons in a U(1) spin liquid. We are inspired by the previous observation of gauge field correlation in the pairwise spin correlation using the neutron scattering measurement when the Dzyaloshinskii-Moriya interaction intertwines with the lattice geometry. We extend this observation to the Lorentz force that exerts on the (neutral) spinons. The external magnetic field, that polarizes the spins, effectively generates an internal U(1) gauge flux for the spinons and twists the spinon motion through the Dzyaloshinskii-Moriya interaction. Such a mechanis…
Emergent Gauge Flux and Spin Ordering in Magnetized Triangular Spin Liquids: Applications to Hofstadter-Hubbard Model
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学北京量子器件重点实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
Tunable Emergent Gauge Fields from Skyrmions in a Quasicrystalline Lattice
Department of Physics and Astronomy, The University of Tennessee（田纳西大学物理与天文学系）；Instituto de Física de Líquidos y Sistemas Biológicos, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata（拉普拉塔国立大学精确科学学院液体与生物系统物理研究所，阿根廷国家科学研究委员会）；Departamento de Ciencias Básicas, Facultad de Ingeniería, UNLP（拉普拉塔国立大学工程学院基础科学系）；Neutron Scattering Division and Shull-Wollan Center, Oak Ridge National Laboratory（橡树岭国家实验室中子散射处和舒尔-沃兰中心）；Centro Atómico Bariloche and Instituto Balseiro, CNEA（巴里洛切原子中心巴尔塞罗研究所，阿根廷核能委员会）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（阿根廷国家科学研究委员会）；Instituto de Nanociencia y Nanotecnología CNEA-CONICET（CNEA-CONICET纳米科学与技术研究所）
We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z2 lattice gauge theory (LGT) which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibits emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial non-interacting peer, and thus is of pure dynamical many-body effect. In this…
A clear separation of the time scales governing the dynamics of "slow" and "fast" degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange coupled to a tight-binding system of (fast) conduction electrons. The effective equations of motion are derived under the constraint that the quantum state of the electron system at any instant of time $t$ lies in the $n$-dimensional low-energy subspace for the corresponding spin configuration at $t$. The effective low-energy theory unfolds itself straightforwa…
