Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods

Abstract

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

111 pages, 54 figures, 6 tables; comments welcome

References in corpus (112)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The numerical renormalization group method for quantum impurity systems
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Theory of Intertwined Orders in High Temperature Superconductors
• Big Data of Materials Science - Critical Role of the Descriptor
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• A class of quantum many-body states that can be efficiently simulated
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• The iTEBD algorithm beyond unitary evolution
• From density-matrix renormalization group to matrix product states
• A one-dimensional liquid of fermions with tunable spin
• Entanglement spectrum in one-dimensional systems
• Spin-charge separation and localization in one-dimension
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• New Trends in Density Matrix Renormalization
• Time-evolving a matrix product state with long-ranged interactions
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Degenerate Fermi Gases of Ytterbium
• Ultracold fermions and the SU(N) Hubbard model
• Measurement-Only Topological Quantum Computation
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• The ODE/IM Correspondence
• Universal theory of nonlinear Luttinger liquids
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
• Spectral functions in one-dimensional quantum systems at T>0
• Direct observation of coherent inter-orbital spin-exchange dynamics
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• An exact mapping between the Variational Renormalization Group and Deep Learning
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Exact diagonalization: the Bose-Hubbard model as an example
• Machine learning for many-body physics: The case of the Anderson impurity model
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Fractional power-law behavior and its origin in iron-chalcogenide and ruthenate superconductors: Insights from first-principles calculations
• Double-degenerate Bose-Fermi mixture of strontium
• Superfluidity and magnetism in multicomponent ultracold fermions
• Infinite size density matrix renormalization group, revisited
• Supplementary material to Heavy electrons and the symplectic symmetry of spin
• Heavy electrons and the symplectic symmetry of spin
• Stability of zero modes in parafermion chains
• Density matrix numerical renormalization group for non-Abelian symmetries
• Collective states of interacting Fibonacci anyons
• BCS pairing in Fermi systems with several flavors
• Chiral Spin Liquids in Arrays of Spin Chains
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• On topological phases of spin chains
• Semi-Inclusive Deep Inelastic Scattering processes from small to large P_T
• Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
• Kondo screening in a magnetically frustrated nanostructure: Exact results on a stable, non-Fermi-liquid phase
• Pairing in a three component Fermi gas
• Covering the Fermi Surface with Patches of Quarkyonic Chiral Spirals
• Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap
• The renormalisation group for the truncated conformal space approach on the cylinder
• NLO Renormalization in the Hamiltonian Truncation
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Superfluidity in a Three-flavor Fermi Gas with SU(3) Symmetry
• Vector chiral order in frustrated spin chains
• Confinement vs Deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• One-point functions in massive integrable QFT with boundaries
• Excited state TBA and renormalized TCSA in the scaling Potts model
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Sine-Gordon form factors in finite volume
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Characterization of resonances using finite size effects
• Co-existence and shell structures of several superfluids in trapped three-component Fermi mixtures
• Luscher's mu-term and finite volume bootstrap principle for scattering states and form factors
• Zero modes method and form factors in quantum integrable models
• Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
• Real-time dynamics in the one-dimensional Hubbard model
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Form factor perturbation theory from finite volume
• Boundary form factors in finite volume
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Competing orders in the generalized Hund chain model at half-filling
• Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model
• Diagonal multi-soliton matrix elements in finite volume
• La${}_2$O${}_3$Fe${}_2$Se${}_2$, a Mott insulator on the brink of orbital-selective metalization
• Surface transport coefficients for three-dimensional topological superconductors
• Matrix product state representation of non-Abelian quasiholes
• A solution of 2D QCD at Finite $N$ using a conformal basis
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Entanglement Entropy from the Truncated Conformal Space
• Sinh-Gordon Boundary TBA and Boundary Liouville Reflection Amplitude
• The particle spectrum of the Tricritical Ising Model with spin reversal symmetric perturbations
• An integrable model with parafermion zero energy modes
• Exact finite volume expectation values of local operators in excited states
• Effective potentials and kink spectra in non-integrable perturbed conformal field theories
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Non-Perturbative Field Theory - From two dimensional conformal field theory to QCD in four dimensions
• Baryon masses in the three-state Potts field theory in a weak magnetic field
• Predicting Excitonic Gaps of Semiconducting Single Walled Carbon Nanotubes From a Field Theoretic Analysis
• Boundary renormalisation group flows of the supersymmetric Lee-Yang model and its extensions
• Strongly Interacting Phases of Metallic Wires in Strong Magnetic Field

Cited by in corpus (69)

• Nonthermal states arising from confinement in one and two dimensions
• Signatures of rare states and thermalization in a theory with confinement
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
• Integrability and dark states in an anisotropic central spin model
• RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Generalized entanglement entropies in two-dimensional conformal field theory
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory
• Exploring Hamiltonian Truncation in $\mathbf{d}=2+1$
• Lightcone Effective Hamiltonians and RG Flows
• Umklapp scattering as the origin of $T$-linear resistivity in the normal state of high-$T_c$ cuprate superconductors
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Kibble-Zurek mechanism in the Ising Field Theory
• Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Hamiltonian truncation in Anti-de Sitter spacetime
• Hamiltonian Truncation Effective Theory
• Emergent conservation laws and nonthermal states in the mixed-field Ising model
• On the low-energy description for tunnel-coupled one-dimensional Bose gases
• Chiral entanglement in massive quantum field theories in 1+1 dimensions
• Perturbative post-quench overlaps in Quantum Field Theory
• Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders
• Chirally Factorised Truncated Conformal Space Approach
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Non-equilibrium aspects of integrable models
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Out-of-horizon correlations following a quench in a relativistic quantum field theory
• Towards a nonperturbative construction of the $S$-matrix
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Hamiltonian Truncation Crafted for UV-divergent QFTs
• Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model
• RG flows on $S^d$ and Hamiltonian truncation
• Topological Quantum Computation on a Chiral Kondo Chain
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Quantum quench in a driven Ising chain
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
• Counterterms in Truncated Conformal Perturbation Theory
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• On asymptotic behaviour in truncated conformal space approach
• Ladder-like optical conductivity in the spin-fermion model
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• On symmetry-resolved generalized entropies
• Sine-Gordon model at finite temperature: the method of random surfaces
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter
• Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
• Current Algebra Approach to 2d Chiral Metals
• On computing non-equilibrium dynamics following a quench
• Emergent SU(3) symmetry in a four leg spin tube
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation
• Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders
• Confinement in the tricritical Ising model