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 statistics. We illustrate this phenomenon through a series of examples including fermionic analogs of both foliated fracton phases and fractal spin liquids. We find that the foliated analogs actually exhibit the same fractonic order as their bosonic counterparts, while this is not generally the case for fermionic fractal spin liquids.
Fractonic phases of matter are novel quantum ground states supporting sub-dimensional emergent excitations with mobility restrictions. Due to a sub-extensive ground state degeneracy that is dependent on the geometry of the underlying lattice, fractonic phases are considered as models for quantum memory or quantum glass. While there exist a number of exactly solvable models with interactions between multiple particles/spins, the realization of such models in real materials is extremely challenging. In this work, we provide a realistic quantum model of quadratic spin interactions on the breathin…
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 …
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.
We show how a finite number of conservation laws can globally `shatter' Hilbert space into exponentially many dynamically disconnected subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a `fractonic' model of quantum dynamics constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in a…
We study the emergence of bosonic pairs in a system of two coupled one-dimensional fermionic chains subject to a gauge flux (two-leg flux ladder), with both attractive and repulsive interaction. In the presence of strong attractive nearest-neighbor interaction and repulsive next-to-nearest-neighbor interaction, the system crosses into a regime in which fermions form tightly bound pairs, which behave as bosonic entities. By means of numerical simulations based on the density-matrix-renormalization-group (DMRG) method, we show in particular that in the strongly paired regime, the gauge flux indu…
We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-co…
Deconfined quantum criticality with emergent SO(5) symmetry in correlated systems remains elusive. Here, by performing numerically-exact state-of-the-art quantum Monte Carlo (QMC) simulations, we show convincing evidences of deconfined quantum critical points (DQCP) between antiferromagnetic and valence-bond-solid phases in the extended Hubbard model of fermions on the honeycomb lattice with large system sizes. We further demonstrate evidences of the SO(5) symmetry at the DQCP. It is important to note that the critical exponents obtained by finite-size scaling at the DQCP here are consistent w…
We introduce a model of Dirac fermions in 2+1 dimensions with a semimetallic, a quantum spin-Hall insulating (QSHI), and an s-wave superconducting (SSC) phase. The phase diagram features a multicritical point at which all three phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC orders correspond to mutually anti-commuting mass terms of the Dirac Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories have been put forward to describe both types of critical points. Using quantum Monte Carlo simulations, we directly study the operator that rotates…
The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-1D strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge $c=2$ and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors.…
Using a hybrid method based on fermionic diagonalization and classical Monte Carlo, we investigate the interplay between itinerant and localized spins, with competing double- and super-exchange interactions, on a honeycomb lattice. For moderate superexchange, a geometrically frustrated triangular lattice of hexagons forms spontaneously. For slightly larger superexchange a dimerized groundstate is stable that has macroscopic degeneracy. The presence of these states on a non-frustrated honeycomb lattice highlights a novel phenomenon in this itinerant electron system: emergent geometrical frustra…
Motivated by recent numerical and experimental studies of the spin-1/2 Heisenberg antiferromagnet on kagome, we formulate a many-body model for fermionic spinons introduced by us earlier [Phys. Rev. Lett. 103, 187203 (2009)]. The spinons interact with an emergent U(1) gauge field and experience strong short-range attraction in the S=0 channel. The ground state of the model is generically a $Z_2$ liquid. We calculate the edge of the two-spinon continuum and compare the theory to the slave-fermion approach to the Heisenberg model.
A significant part of the phase diagram of the two-dimensional fermionic Hubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$) is governed by effective Fermi liquid physics with weak BCS-type instabilities. We access this regime in a controlled way by a combination of the bold-line diagrammatic Monte Carlo method with an additional ladder-diagram summation trick and semi-analytic treatment of the weak instability in the Cooper channel. We obtain the corresponding ground-state phase diagram in the $(n,U)$ plane describing the competition between the $p-$ and $d-$wave s…
Recently, it was shown that strongly correlated metallic fermionic systems [Nature Phys. 3, 168 (2007)] generically display kinks in the dispersion of single fermions without the coupling to collective modes. Here we provide compelling evidence that the physical origin of these kinks are emerging internal collective modes of the fermionic systems. In the Hubbard model under study these modes are identified to be spin fluctuations which are the precursors of the spin excitations in the insulating phase. In spite of their damping the emergent modes give rise to signatures very similar to feature…
The Fermi-point scenario of emergent gravity has the following consequences: gravity emerges together with fermionic and bosonic matter; emergent fermionic matter consists of massless Weyl fermions; emergent bosonic matter consists of gauge fields; Lorentz symmetry persists well above the Planck energy; space-time is naturally 4-dimensional; Universe is naturally flat; cosmological constant is naturally small or zero; underlying physics is based on discrete symmetries; `quantum gravity' cannot be obtained by quantization of Einstein equations; there is no contradiction between quantum mechanic…
We reconsider monolayer graphene in the presence of elastic deformations. It is described by the tight - binding model with varying hopping parameters. We demonstrate, that the fermionic quasiparticles propagate in the emergent 2D Weitzenbock geometry and in the presence of the emergent U(1) gauge field. Both emergent geometry and the gauge field are defined by the elastic deformation of graphene.
Quantum degeneracy pressure (QDP) underscores the stability of matter and is arguably the most ubiquitous many-body effect. The associated Fermi surface (FS) has broad implications for physical phenomena, ranging from electromagnetic responses to entanglement entropy (EE) area law violations. Given recent fruitful studies in condensed-matter physics under effectively non-Hermitian descriptions, it becomes urgent to study how QDP and many-body interactions interplay with non-Hermitian effects. Through a prototypical critical 1D fermionic lattice with asymmetric gain/loss, a real space FS is sho…
A central problem in quantum condensed matter physics is the critical theory governing the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. We present here results showing that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute the spectral functions of fermions in the field theor…
We study an interface between a Kitaev spin liquid (KSL) in the chiral phase and a non-chiral superconductor. When the coupling across the interface is sufficiently strong, the interface undergoes a transition into a phase characterized by a condensation of a bound state of a Bogoliubov quasiparticle in the superconductor and an emergent fermionic excitation in the spin liquid. In the condensed phase, electrons in the superconductor can coherently convert into emergent fermions in the spin liquid and vice versa. As a result, the chiral Majorana edge mode of the spin liquid becomes visible in t…
We study the renormalization group flow of the velocities in the field theory describing the coupling of the massless quasi-relativistic fermions to the bosons through the Yukawa coupling, as well as with both bosons and fermions coupled to a fluctuating $U(1)$ gauge field in two and three spatial dimensions. Different versions of this theory describe quantum critical behavior of interacting Dirac fermions in various condensed-matter systems. We perform an analysis using one-loop $ε-$expansion about three spatial dimensions, which is the upper critical dimension in the problem. In two dimensio…
Deep learning emergent spacetime from fermionic spectral functions in holography
Kyoto University（京都大学）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Pohang University of Science and Technology（浦项科技大学）；Gwangju Institute of Science and Technology（光州科学技术院）
Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-order $ε$ expansion in $4-ε$ dimensions, we study the critical structure and emergent symmetry of the chiral GNY model with $N_f$ flavors of four-component Dirac fermions coupled strongly to an $O(N)$ scalar field under a small $O(N)$-symmetry breaking perturbation. After determining the stable fixed…
Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice $\mathbb{Z}_4$ parafermions and lattice spin-$1/2$ fermions which preserves the locality of operators with $\mathbb{Z}_4$ symmetry. Based on this mapping, we construct an exactly solvable, local, and interacting one-dimensional fermionic Hamiltonian which hosts zero-energy modes obeying parafermionic algebra. We numerically show that this parafermionic phase remains stable in a wide…
We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of 7 families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric/magnetic charges. We show how these spin liquids are related to each other. Two of these classes admit nontrivial protected surface states which we describe. We show how to access all of the 7 spin liquids through slave particle (parton) constructions. We also provide intuitive loop gas descriptions of their ground state wave functions. One of these phases is the `topological Mott ins…
We consider the stability of nodal surfaces in fermionic band systems with respect to the Coulomb repulsion. It is shown that nodal surfaces at the Fermi level are gapped out at low temperatures due to emergent particle-hole orders. Energy dispersion of the nodal surface suppresses the instability through an inhomogenous phase. We argue that around criticality the order parameter fluctuations can induce superconductivity. We show that by tuning doping and disorder one could access various phases, establishing fermionic nodal surface systems as a versatile platform to study emergent quantum ord…
The phenomenon of emergent physics in condensed-matter many-body systems has become the paradigm of modern physics, and can probably also be applied to high-energy physics and cosmology. This encouraging fact comes from the universal properties of the ground state (the analog of the quantum vacuum) in fermionic many-body systems, described in terms of the momentum-space topology. In one of the two generic universality classes of fermionic quantum vacua the gauge fields, chiral fermions, Lorentz invariance, gravity, relativistic spin, and other features of the Standard Model gradually emerge at…
Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions, we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians proposed by Haah. We prove that given a translation-invariant fermionic system with general $q$-body interactions, where $q$ is even, a local mapping preserving global fermion parity to a dual Pauli spin model exists and is unique up to a choice of basis. Furthermore, the dual spin model is constructive, and we present various examples of these dualities. As an application, we bosonize fermionic s…
We study the physics of 3d supersymmetric abelian gauge theories (with small supersymmetry breaking perturbations) at finite density. Using mirror symmetry, which provides a natural generalization of the duality between the XY model and the abelian Higgs model but now including fermionic fields, we see many dynamical phenomena conjectured to be of relevance in condensed matter systems. In particular, we find examples of the emergence of a Fermi surface at low energies from hybridization of fermions localized at magnetic defects at high energies, as well as fractionalization of charged fermions…
We present the calculation of the coherent spectral functions and density of states (DOS) for excitonic systems in the frame of the three dimensional extended Falicov-Kimball model. By using gauge-invariant U(1) transformation to the usual fermions, we represent the electron operator as a fermion attached to the U(1) phase-flux tube. The emergent bosonic gauge field, related to the phase variables is crucial for the Bose-Einstein condensation (BEC) of excitons. Employing the path-integral formalism, we manipulate the bosonic and fermionic degrees of freedom to obtain the effective actions rela…
When a fermionic quantum Hall system is projected into the lowest Landau level, there is an exact particle-hole symmetry between filling fractions $ν$ and $1-ν$. We investigate whether a similar symmetry can emerge in bosonic quantum Hall states, where it would connect states at filling fractions $ν$ and $2-ν$. We begin by showing that the particle-hole conjugate to a composite fermion `Jain state' is another Jain state, obtained by reverse flux attachment. We show how information such as the shift and the edge theory can be obtained for states which are particle-hole conjugates. Using the tec…
Using Quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with $N$ flavors of fermions per site for $N=1,2$ and $3$. The models have an extensive number of conserved quantities but are not integrable, and have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond Landau-Ginzburg paradigm. In particular, one of the prominent phase for $N>1$ corresponds to $2N$ gapless Dirac fermions coupled to an emergent $\mathbb{Z}_2$ gauge field in its deconfined phase. However, unlike a con…
Unifying Dirac Spin Liquids on Square and Shastry-Sutherland Lattices via Fermionic Deconfined Criticality
Universität Würzburg（维尔茨堡大学）；Flatiron Institute（平顿研究所）；Massachusetts Institute of Technology（麻省理工学院）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Harvard University（哈佛大学）
Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $α$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $ω$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $ω$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low…
In this work we provide for a description of the low-energy physics of interacting multi-species fermions in terms of the bound-states that are stabilized in these systems when a spin gap opens. We argue that, at energies much smaller than the spin gap, these systems are described by a Luttinger liquid of bound-states that depends, on top of the charge stiffness $ν$ and the charge velocity $u$, on a "Fermi" momentum $P_F$ satisfying $qP_F = Nk_F$ where $q$ is the charge of the bound-state, $N$ the number of species and $k_F$ is the Fermi momentum in the non-interacting limit. We further argue …
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu$^\ast$ universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-…
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 …
Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidences of it have been revealed in nature yet. In this letter, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably-doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using renormalization group, we theoretically show that N=2 sp…
We report on spectroscopy study of elementary magnetic excitations in an Ising-like antiferromagnetic chain compound SrCo$_2$V$_2$O$_8$ as a function of temperature and applied transverse magnetic field up to 25 T. An optical as well as an acoustic branch of confined spinons, the elementary excitations at zero field, are identified in the antiferromagnetic phase below the Néel temperature of 5 K and described by a one-dimensional Schrödinger equation. The confinement can be suppressed by an applied transverse field and a quantum disordered phase is induced at 7 T. In this disordered paramagnet…
We investigate the electronic properties of the boson mode in a three-point fermion loop. In this framwork, the single-particle excitation and the many-body local (in imaginary time and momentum space) field effects are investigated in IR or UV limits with the density fluctuation induced by external potential (or bosonic frequency). While in the limit of vanishing effect of external potential, which is equivalent to UV limit of the fermionic frequency, the conserving approximation can be applied together with the Luttinger-Ward analysis, in which case the anomalous contribution to the fermion …
CeTe3 is a unique platform to investigate the itinerant magnetism in a van der Waals (vdW) coupled metal. Despite chemical pressure being a promising route to boost quantum fluctuation in this system, a systematic study on the chemical pressure effect on Ce3+(4f1) states is absent. Here, we report on the successful growth of a series of Se doped single crystals of CeTe3. We found a fluctuation driven exotic magnetic rotation from the usual easy-axis ordering to an unusual hard-axis ordering. Unlike in localized magnetic systems, near-critical magnetism can increase itinerancy hand-in-hand with…
Unraveling the Emergence of Slow Dynamics in U(1) Lattice Gauge Theories
International School for Advanced Studies (SISSA)（高级研究国际学院）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文系）；INFN, sezione di Bologna（意大利国家核物理研究所博洛尼部分部）
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 study a model for a quantum critical point in two spatial dimensions between a semimetallic phase, characterized by a stable quadratic Fermi node, and an ordered phase, in which the spectrum develops a band gap. The quantum critical behavior can be computed exactly, and we explicitly derive the scaling laws of various observables. While the order-parameter correlation function at criticality satisfies the usual power law with anomalous exponent $η_ϕ= 2$, the correlation length and the expectation value of the order parameter exhibit essential singularities upon approaching the quantum criti…
We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is oppos…
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo si…
