Large-N volume independence in circle-compactified QCD with N_f \geq 1 adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N_f=1 supersymmetric case. Resolution of the tension for N_f>1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N=\infty theory is free, with a trivial S-matrix. We show an example of such a spectral degeneracy in a non-supersymmetric toy example which has a Hagedorn spectrum.
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…
We study, by using tools of the dynamical system theory, a fermionic string streched from a non-commutative D2-brane (stack of D0-branes in the BFSS model) to a probe D0-brane as a quantum system driven by a chaotic system, the (classical and quantum) chaos being induced in the D2-brane dynamics by quantum fluctuations. We show that this dynamics with fluctuations induces a decoherence phenomenon on the reduced density matrix of the fermionic string which is characteristic of the chaotic behaviour since it presents an horizon of coherence. Moreover we show that this dynamics is associated with…
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）
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…
In a fermionic quantum vacuum, the parameters k_μof a CPT-violating Chern-Simons-like action term induced by CPT-violating parameters of the fermionic sector depend on the universality class of the system. As a concrete example, we consider the Dirac Hamiltonian of a massive fermionic quasiparticle and add a particular term with purely-spacelike CPT-violating parameters b_μ=(0,{\bf b}). A quantum phase transition separates two phases, one with a fully-gapped fermion spectrum and the other with topologically-protected Fermi points (gap nodes). The emergent Chern-Simons ``vector'' k_μ=(0,{\bf k}…
We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are interested in the field theory in $R\cup L$ to understand the long range quantum correlations between $R$ and $L$. There are local modes of the Dirac field having supports individually either in $R$ or $L$, as well as global modes found via analytically continuing the $R$ modes to $L$ and vice versa. However, we show that unlike the case of a scalar field, …
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…
Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；DIPC - Donostia International Physics Center（多诺西亚国际物理中心）；Birla Institute of Technology and Science, Pilani Campus（比拉理工与科学学院皮拉尼校区）
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 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 $t$-…
A central theme in many body physics is emergence - new properties arise when several particles are brought together. Particularly fascinating is the idea that the quantum statistics may be an emergent property. This was first noted in the Skyrme model of nuclear matter, where a theory formulated entirely in terms of a bosonic order parameter field contains fermionic excitations. These excitations are smooth field textures, and believed to describe neutrons and protons. We argue that a similar phenomenon occurs in topological insulators when superconductivity gaps out their surface states. Her…
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）
Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme developed in a companion work (Ref.[1]) to the study of two archetypal models of stongly correlated lattice electrons, one with translation invariance and one without. We obtain detailed insight into the emergence of various gapless and gapped phases of quantum electronic matter by computing effective Hamiltonians as well as entanglement signatures through their r…
We examine the interplay of symmetry and topological order in $2+1$ dimensional fermionic topological phases of matter. We define fermionic topological symmetries acting on the emergent topological effective theory described using braided tensor category theory. Connecting this to the ${\cal G}^{\rm f}$ fermionic symmetry of the microscopic physical system, we characterize and classify symmetry fractionalization in fermionic topological phases. We find that the physical fermion provides constraints that result in a tiered structure of obstructions and classification of fractionalization with r…
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 analyze the possibility of emergent quantum multicritical points (MCPs) with enlarged chiral symmetry, when strongly interacting gapless Dirac fermions acquire comparable propensity toward the nucleation of Kekulé valence-bond solid (KVBS) and charge-density-wave ($N_b=1$) or $s$-wave pairing ($N_b=2$) or anti-ferromagnet ($N_b=3$) in honeycomb lattice, where $N_b$ counts the number of bosonic order parameter components. Besides the cubic terms present in the order parameter description of KVBS due to the breaking of a discrete $Z_3$ symmetry, quantum fluctuations generate new cubic vertice…
We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call "m-type" and "q-type" particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have n…
Recently, there is a considerable study on gapped symmetric phases of bosons that do not break any symmetry. Even without symmetry breaking, the bosons can still be in many exotic new states of matter, such as symmetry-protected trivial (SPT) phases which are short-range entangled and symmetry-enriched topological (SET) phases which are long-range entangled. It is well-known that non-interacting fermionic topological insulators are SPT states protected by time-reversal symmetry and U(1) fermion number conservation symmetry. In this paper, we construct three-dimensional exotic phases of bosons …
In this letter, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gau…
Fractional quantum Hall (FQH) system at Landau level filling fraction $ν=5/2$ has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance $σ_{xy}=5e^2/2h$. Thermal Hall conductances of the Pf and APf states are quantized at $κ_{xy}=7/2$ and $κ_{xy}=3/2$ respectively in a proper unit. However, a recent experiment shows the thermal Hall conductance of $ν=5/2$ FQH state is $κ_{xy}=5/2$. It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Maj…
