Truncated Hilbert space approach to the 2d ${\varphi }^4$ theory

Abstract

We apply the massive analogue of the truncated conformal space approach to study the two dimensional ${\varphi }^4$ theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We interpret the results in terms of the Bethe-Yang spectrum, from which we extract the infinite volume masses and scattering matrices for various couplings. We compare these results against semiclassical analysis and perturbation theory. We also analyze the critical point of the model and confirm that it is in the Ising universality class.

pdflatex, 35 pages with 29 pdf figures. Binary program is also attached, run on linux as: phi4 config.dat, v2: typos corrected, comparison to other works and references added, vacuum splitting analysis corrected, comparison to sine-Gordon TCSA added, v3: improved numerics, analysis on excited kink added, critical point investigated

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Cited by in corpus (34)

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• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• 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
• 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
• Kibble-Zurek mechanism in the Ising Field Theory
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Hamiltonian Truncation Effective Theory
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• False vacuum decay in the 1+1 dimensional ${\phi }^4$ theory
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Leading exponential finite size corrections for non-diagonal form factors
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Towards a nonperturbative construction of the $S$-matrix
• Bound states in Functional Renormalization Group
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Critical behavior of the 2d scalar theory: resumming the ${\mathrm{N}}^8\mathrm{LO}$ perturbative mass gap
• Cut-Off Kinks
• The semiclassical energy density of kinks and solitons
• Topological Defects in Quantum Field Theory with Matrix Product States
• Non-equilibrium time evolution in the sine-Gordon model revisited
• Hamiltonian formulation of the $1+1$-dimensional ${\varphi }^4$ theory in a momentum-space Daubechies wavelet basis
• On computing non-equilibrium dynamics following a quench
• Weak vs. strong breaking of integrability in interacting scalar quantum field theories
• A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime
• Relaxation dynamics in the (double) sine-Gordon model: An open-system viewpoint