Studying Continuous Symmetry Breaking using Energy Level Spectroscopy

2017/04/27 by Alexander Wietek, Michael Schüler, Wietek, Alexander +3 · 4 citations
Engineering · Materials Science · #Power Transformer Diagnostics and Insulation #Electron and X-Ray Spectroscopy Techniques

paper · pdf · doi:10.48550/arxiv.1704.08622

Abstract

Tower of States analysis is a powerful tool for investigating phase transitions in condensed matter systems. Spontaneous symmetry breaking implies a specific structure of the energy eigenvalues and their corresponding quantum numbers on finite systems. In these lecture notes we explain the group representation theory used to derive the spectral structure for several scenarios of symmetry breaking. We give numerous examples to compute quantum numbers of the degenerate groundstates, including translational symmetry breaking or spin rotational symmetry breaking in Heisenberg antiferromagnets. These results are then compared to actual numerical data from Exact Diagonalization.

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• Gradient-based search of quantum phases: discovering unconventional fractional Chern insulators
• Ab initio spin Hamiltonians and magnetism of Ce and Yb triangular-lattice compounds

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