Extracting the Speed of Light from Matrix Product States

Abstract

We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e.~the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical $SU(2)$ Heisenberg chains with half-integer spin $S>1/2$ with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions.

6 pages, 4 figures, 1 table, published version

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• Low-temperature Gibbs states with tensor networks
• Continuous Wigner-Mott transition at $\nu =1/5$
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Probing universal critical scaling with scan-DMRG
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Using magnetic dynamics to measure the spin gap in a candidate Kitaev material
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition