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arXiv · 2310.15759

2D excitation information by MPS method on infinite helixes

Xing-Yu Zhang·Runze Chi·Yang Liu·Lei Wang
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Abstract

Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems.

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Xing-Yu Zhang, Runze Chi, Yang Liu, Lei Wang. 2023-10-24. 2D excitation information by MPS method on infinite helixes. https://doi.org/10.1103/physrevb.109.075129

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