Detecting spontaneous symmetry breaking and bound states in (1+1)-dimensional bosonic models with lightcone conformal truncation
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Abstract
Lightcone Conformal Truncation (LCT) is a relatively new Hamiltonian truncation method that proposes viewing QFTs as deformations of solvable conformal field theories (CFTs). LCT stands out from other truncation methods in fully preserving conformal invariance and probing the infinite volume limit directly. The output of the method is a discretized version of the spectrum of the underlying continuum theory, which can subsequently be used to calculate other QFT observables. We apply the method to two bosonic scalar field theories, with a quartic/sextic potential described by two dimensionless couplings. The theories exhibit textbook Landau-Ginzburg first order phase transitions at weak coupling, providing an ideal laboratory for the method to probe observables at criticality. The 𝜙⁴ theory requires the ℤ₂ symmetry to be broken by a 𝜙³ term to access the SSB phase, while the 𝜙⁶ theory requires no explicit breaking. We identify a method to detect a phase transition with our method and we present novel, quantitative, non-perturbative estimates for the shape of the phase transition lines and furthermore, we detect and quantify the emergence and weak coupling dependence of the bound states in the spectrum of the theories.
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2024
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Attribution 4.0 International