2017/06/30 by Tianci Zhou, Mao Lin
Mathematics · Physics and Astronomy · #Bipartite graph #Boundary (topology) #Boundary conformal field theory #Boundary value problem #Combinatorics #Conformal map #Critical exponent #Exponent #Luttinger liquid #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Parameterized complexity #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Robin boundary condition #Singularity #Topological Materials and Phenomena #Type (biology) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.96.245409
published as Phys. Rev. B 96, 245409 (2017) · v1: 18 pages, 12 figures v2: more detailed conformal mapping analysis, clarification on the corrections in the free energy, appendices reordered
arxiv created 2017/12/13 · openalex publication_date 2017/12/13 · arxiv updated 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the quantum quench problem for a class of bosonic conformal interfaces by computing the Loschmidt echo and the bipartite fidelity. The quench can be viewed as a sudden change of boundary conditions parametrized by \ensuremathθ when connecting two one-dimensional critical systems. They are classified by S(\ensuremathθ) matrices associated with the current scattering processes on the interface. The resulting Loschmidt echo of the quench has long time algebraic decay t^\ensuremath-\ensuremathα, whose exponent also appears in the finite size bipartite fidelity as L^\ensuremath-\frac\ensuremathα2. We perform analytic and numerical calculations of the exponent \ensuremathα, and find that it has a quadratic dependence on the change of \ensuremathθ if the prior and post-quench boundary conditions are of the same type of S, while remaining (1)/(4) otherwise. Possible physical realizations of these interfaces include, for instance, connecting different quantum wires (Luttinger liquids), quench of the topological phase edge states, etc., and the exponent can be detected in an x-ray edge singularity-type experiment.