Universality of a truncated sigma-model

• URL: http://arxiv.org/abs/2109.07500v1
• Date: Wed, 15 Sep 2021 18:06:07 GMT
• Title: Universality of a truncated sigma-model
• Authors: Andrei Alexandru, Paulo F. Bedaque, Andrea Carosso, Andy Sheng
• Abstract summary: Even when regularized using a finite lattice, Bosonic quantum field theories possess an infinite dimensional Hilbert space. A qubitization of the $1+1$ dimensionalally free $sigma$-model based on ideas of non-commutative geometry was previously proposed. We provide evidence that it reproduces the physics of the $sigma$-model both in the infrared and the ultraviolet regimes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert space is then needed and the physical results are obtained after a double limit: one to remove the truncation and another to remove the regulator (the continuum limit). A simpler alternative is to find a model with a finite dimensional Hilbert space belonging to the same universality class as the continuum model (a "qubitization"), so only the space continuum limit is required. A qubitization of the $1+1$ dimensional asymptotically free $O(3)$ nonlinear $\sigma$-model based on ideas of non-commutative geometry was previously proposed arXiv:1903.06577 and, in this paper, we provide evidence that it reproduces the physics of the $\sigma$-model both in the infrared and the ultraviolet regimes.

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