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arXiv:2509.17975

Optimal local basis truncation of lattice quantum many-body systems

Peter Majcen, Giovanni Cataldi, Pietro Silvi, Simone Montangero

Published Sep 22, 2025• 0 citations
arXivHTMLPDF

Abstract

We show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate and numerically stable across different model phases, even close to quantum phase transitions. We apply this procedure to different models, such as the Sine-Gordon model, the $φ^{4}$ theory, and lattice gauge theories, namely Abelian $\mathrm{U}(1)$ and non-Abelian $\mathrm{SU}(2)$, in one and two spatial dimensions. Our results reduce state-of-the-art estimates of computational resources for classical and quantum simulations.

DOI
10.48550/arxiv.2509.17975

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We show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate and numerically stable across different model phases, even close to quantum phase transitions. We apply this procedure to different models, such as the Sine-Gordon model, the φ4φ^{4}φ4 theory, and lattice gauge theories, namely Abelian U(1)\mathrm{U}(1)U(1) and non-Abelian SU(2)\mathrm{SU}(2)SU(2), in one and two spatial dimensions. Our results reduce state-of-the-art estimates of computational resources for classical and quantum simulations.
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Quantum simulations of lattice gauge theories with continuous gauge groups require a choice of basis (how states of the gauge theory map to the qubit computational basis) and truncation scheme (which of the infinitely many gauge theory basis states should be omitted in the map to the finite dimensional qubit Hilbert space.) The most common choices are adapted to an electric basis for the gauge theory, where the basis states for each link are associated with irreducible representations of the gauge group. Electric bases and truncations are generally advantageous for preserving gauge symmetries and simulating the strong coupling regime, but their effectiveness in the weak coupling regimes of physical interest are less well understood. In this work, we compute relative probabilities p(R′)/p(R)p(R')/p(R)p(R′)/p(R) for finding a link in the irreps R,R′R,R'R,R′ in the ground state of SU(3) lattice gauge theory using Euclidean Monte Carlo methods and weak-coupling lattice perturbation theory. The observables that compute these relative probabilities are constructed by introducing seams into an anisotropic lattice, and by a similar construction we are also able to measure relative probabilities of different site singlets (ways that electric flux braids together into a gauge singlet) at each vertex. With these methods we can quantify, for example, the importance of higher electric flux states in the weak coupling ground state. These results directly inform what truncations are needed to accurately capture non-abelian gauge dynamics near the continuum limit.
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