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arXiv:cond-mat/9709244 · Springer eBooks

Gauge Theory Description of Spin Chains and Ladders

Yutaka Hosotani

Published Jan 1, 2000• 0 citations
arXivHTMLPDF
DOI
10.1007/978-1-4612-1254-6_10

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Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.
An antiferromagnetic spin chain is equivalent to the two-flavour massless Schwinger model in a uniform background charge density in the strong coupling regime. The gapless mode of the spin chain is represented by a massless boson of the Schwinger model. In a two-leg spin ladder system the massless boson aquires a finite mass due to inter-chain interactions. The gap energy is found to be about when the inter-chain Heisenberg coupling is small compared with the intra-chain Heisenberg coupling. It is also shown that a cyclically symmetric -leg ladder system is gapless or gapful for an odd or even , respectively.
Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.