Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories

Abstract

We study the spectrum of Landau-Ginzburg theories in 1+1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reproduce the expected spectrum of a ${\Phi }^2$ theory (i.e. a free massive boson) in this framework. We then turn to ${\Phi }^4$ in its unbroken phase and compare our numerical results with the predictions of two-loop perturbation theory, finding excellent agreement. We then analyze the broken phase of ${\Phi }^4$ where kink excitations together with their bound states are present. We confirm the semiclassical predictions for this model on the number of stable kink-antikink bound states. We also test the semiclassics in the double well phase of ${\Phi }^6$ Landau-Ginzburg theory, again finding agreement.

arXiv comment29 pages, 12 figures, v2: added discussion about the parameter beta, added references, other minor changes, published version

References in corpus (18)

• Constructing the generalized Gibbs ensemble after a quantum quench
• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• Non-integrable aspects of the multi-frequency Sine-Gordon model
• Truncated Conformal Space at c=1, Nonlinear Integral Equation and Quantization Rules for Multi-Soliton States
• g-function flow in perturbed boundary conformal field theories
• A Numerical Renormalization Group for Continuum One-Dimensional Systems
• Nonperturbative study of the two-frequency sine-Gordon model
• Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory
• Excited state TBA and renormalized TCSA in the scaling Potts model
• Energy Level Distribution of Perturbed Conformal Field Theories
• Neutral Bound States in Kink-like Theories
• Truncated Conformal Space Approach for Perturbed Wess-Zumino-Witten $SU(2{)}_k$ Models
• Finite-Volume Form Factors in Semiclassical Approximation
• On the renormalisation group for the boundary Truncated Conformal Space Approach
• Particle spectrum of the 3-state Potts field theory: a numerical study
• Exciton Hierarchies in Gapped Carbon Nanotubes
• A Renormalization Group For Treating 2D Coupled Arrays of Continuum 1D Systems
• The particle spectrum of the Tricritical Ising Model with spin reversal symmetric perturbations

Cited by in corpus (34)

• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• A Cheap Alternative to the Lattice?
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• Hamiltonian truncation approach to quenches in the Ising field theory
• Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• A Conformal Truncation Framework for Infinite-Volume Dynamics
• Quench dynamics of the Ising field theory in a magnetic field
• RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Lightcone Effective Hamiltonians and RG Flows
• Confinement in the q-state Potts model: an RG-TCSA study
• Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group
• Kibble-Zurek mechanism in the Ising Field Theory
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• False vacuum decay in the 1+1 dimensional ${\phi }^4$ theory
• Exact finite volume expectation values of local operators in excited states
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Leading exponential finite size corrections for non-diagonal form factors
• The renormalized Hamiltonian truncation method in the large $E_T$ expansion
• The Two-Loop ${\varphi }^4$ Kink Mass
• Towards a nonperturbative construction of the $S$-matrix
• The semiclassical energy density of kinks and solitons
• The ${\varphi }^4$ Kink Mass at Two Loops
• On computing non-equilibrium dynamics following a quench
• Weak vs. strong breaking of integrability in interacting scalar quantum field theories
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation
• Relaxation dynamics in the (double) sine-Gordon model: An open-system viewpoint
• The AdS/CFT partition function, AdS as a lift of a CFT, and holographic RG flow from conformal deformations