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Exact duality relations in correlated electron systems.

Tsutomu Momoi1, Toshiya Hikihara

  • 1Condensed-Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan.

Physical Review Letters
|February 3, 2004
PubMed
Summary

Exact duality relations between electron system orders were derived using gauge transformations. These findings reveal mappings between conventional and unconventional density-wave orders in Hubbard ladders.

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Area of Science:

  • Condensed matter physics
  • Quantum magnetism
  • Strongly correlated electron systems

Background:

  • Understanding the complex behavior of correlated electron systems is crucial in condensed matter physics.
  • Identifying and classifying different electronic orders, such as density waves, is key to mapping their phase diagrams.
  • Gauge transformations offer a powerful, yet underutilized, tool for uncovering hidden symmetries and relationships.

Purpose of the Study:

  • To derive exact duality relations between various order parameters in correlated electron systems.
  • To apply these relations to the generalized two-leg Hubbard ladder model.
  • To establish mappings between conventional and unconventional density-wave orders.

Main Methods:

  • Gauge transformations were applied to electron bond operators.
  • The generalized two-leg Hubbard ladder model was analyzed at arbitrary filling.
  • Duality relations were systematically derived and investigated.

Main Results:

  • Two exact duality relations were identified in the generalized two-leg Hubbard ladder.
  • Unconventional density-wave orders (staggered flux, circulating spin current) were shown to be dual to conventional density-wave orders.
  • Direct mappings between these dual phases were established.

Conclusions:

  • The derived duality relations provide new insights into the phase diagram of correlated electron systems.
  • Gauge transformations offer a systematic approach to understanding complex electronic orders.
  • The findings facilitate a deeper comprehension of phase transitions and emergent phenomena in Hubbard models.

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