Problems With the Vortex-Boson Mapping in 1+1 Dimensions
Leon Balents, Steven H. Simon
TL;DR
This paper examines the limitations of the vortex-boson mapping in 1+1 dimensions, highlighting the importance of limit order in calculating tilt response and its implications for understanding flux vortex systems.
Contribution
It identifies issues with the vortex-boson mapping in 1+1 dimensions and clarifies the correct approach to calculating tilt response in disorder-free systems.
Findings
The tilt response calculation requires a specific order of limits.
The vortex-boson mapping has subtle limitations in 1+1 dimensions.
Proper limit handling avoids misleading results.
Abstract
Using the well known boson mapping, we relate the transverse magnetic susceptibility of a system of flux vortices in 1+1 dimensions to an appropriately defined conductivity of a one-dimensional boson system. The tilt response for a system free of disorder is calculated directly, and it is found that a subtle order of limits is required to avoid deceptive results.
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