Using gauge transformations on electron bond operators, we derive exact duality relations between various order parameters for correlated electron systems. Applying these transformations, we find two duality relations in the generalized two-leg Hubbard ladder at arbitrary filling. The relations show that unconventional density-wave orders such as staggered flux or circulating spin current are dual to conventional density-wave orders and there are direct mappings between dual phases. Several exact results on the phase diagram are also concluded.Using gauge transformations on electron bond operators, we derive exact duality relations between various order parameters for correlated electron systems. Applying these transformations, we find two duality relations in the generalized two-leg Hubbard ladder at arbitrary filling. The relations show that unconventional density-wave orders such as staggered flux or circulating spin current are dual to conventional density-wave orders and there are direct mappings between dual phases. Several exact results on the phase diagram are also concluded.

arXiv:cond-mat/0310574Physical Review LettersDec 18, 200311 citations

Quantum fluctuations in correlated electron systems

Nayana Shah

Jan 1, 20030 citations

Duality Relations and Exotic Orders in Electronic Ladder Systems

Tsutomu Momoi, Toshiya Hikihara

We discuss duality relations in correlated electronic ladder systems to clarify mutual relations between various conventional and unconventional phases. For the generalized two-leg Hubbard ladder, we find two exact duality relations, and also one asymptotic relation which holds in the low-energy regime. These duality relations show that unconventional (exotic) density-wave orders such as staggered flux or circulating spin-current are directly mapped to conventional density-wave orders, which establishes the appearance of various exotic states with time-reversal and/or spin symmetry breaking. We also study duality relations in the SO(5) symmetry that was proposed to unify antiferromagnetism and d-wave superconductivity. We show that the same SO(5) symmetry also unifies circulating spin current order and s-wave superconductivity.We discuss duality relations in correlated electronic ladder systems to clarify mutual relations between various conventional and unconventional phases. For the generalized two-leg Hubbard ladder, we find two exact duality relations, and also one asymptotic relation which holds in the low-energy regime. These duality relations show that unconventional (exotic) density-wave orders such as staggered flux or circulating spin-current are directly mapped to conventional density-wave orders, which establishes the appearance of various exotic states with time-reversal and/or spin symmetry breaking. We also study duality relations in the SO(5) symmetry that was proposed to unify antiferromagnetism and d-wave superconductivity. We show that the same SO(5) symmetry also unifies circulating spin current order and s-wave superconductivity.

arXiv:cond-mat/0412610Journal of the Physical Society of JapanJan 1, 20053 citations

Manifestation of quantum fluctuations in strongly correlated systems

Anatoli Polkovnikov

Jan 1, 20030 citations

Block entanglement and fluctuations in finite-size correlated electron systems

Archak Purkayastha, V. Subrahmanyam

The block entanglement entropy and fluctuations are investigated in one dimension in finite-size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic divergence for all values of the correlation projection parameter $g$ , as predicted by conformal field theories for critical systems, but the central charge requires finite-size corrections. There is an infinite correlation length corresponding to correlation between the same kinds of spins, for all values of $g$ . A scaling form for the block entropy, as a function of $g$ and the system size $N$ , is proposed which predicts a metal-insulator crossover at ${N}^{1/3}g\ensuremath{\approx}0.24$ for $N<{10}^{5}$ . Bipartite fluctuations in the number of particles in a block, and the spin fluctuations also obey an approximate scaling. A relation is found between the block entropy and the bipartite spin fluctuations. Our results show some correspondence with an experiment on Ni nanochains.The block entanglement entropy and fluctuations are investigated in one dimension in finite-size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic divergence for all values of the correlation projection parameter $g$, as predicted by conformal field theories for critical systems, but the central charge requires finite-size corrections. There is an infinite correlation length corresponding to correlation between the same kinds of spins, for all values of $g$. A scaling form for the block entropy, as a function of $g$ and the system size $N$, is proposed which predicts a metal-insulator crossover at ${N}^{1/3}g\ensuremath{\approx}0.24$ for $N<{10}^{5}$. Bipartite fluctuations in the number of particles in a block, and the spin fluctuations also obey an approximate scaling. A relation is found between the block entropy and the bipartite spin fluctuations. Our results show some correspondence with an experiment on Ni nanochains.

arXiv:1307.1781Physical Review BMay 19, 20145 citations

g

, as predicted by conformal field theories for critical systems, but the central charge requires finite-size corrections. There is an infinite correlation length corresponding to correlation between the same kinds of spins, for all values of

g

. A scaling form for the block entropy, as a function of

g

and the system size

N

, is proposed which predicts a metal-insulator crossover at ${N}^{1/3}g\ensuremath{\approx}0.24$ for

N<{10}^{5}

. Bipartite fluctuations in the number of particles in a block, and the spin fluctuations also obey an approximate scaling. A relation is found between the block entropy and the bipartite spin fluctuations. Our results show some correspondence with an experiment on Ni nanochains.