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arXiv:0809.3569 · Physical Review B

Quantum phase transition in the one-dimensional period-two and uniform compass model

Kewei Sun, Yuyu Zhang, Qing‐Hu Chen

Published Mar 25, 2009• 30 citations
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Abstract

Quantum phase transitions in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudospin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudospin entanglement, spin and pseudospin-correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudospin concurrence is observed, which scales as $1/N$ ($N$ is the system size). The spin-correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudospin-correlation functions exhibit an oscillating behavior, which is absent in the uniform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.

DOI
10.1103/physrevb.79.104429

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Quantum phase transitions in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudospin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudospin entanglement, spin and pseudospin-correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudospin concurrence is observed, which scales as 1/N1/N1/N (NNN is the system size). The spin-correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudospin-correlation functions exhibit an oscillating behavior, which is absent in the uniform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.
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We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions σizσi+1zσ_i^zσ_{i+1}^zσiz​σi+1z​ and σixσi+1xσ_i^xσ_{i+1}^xσix​σi+1x​, alternating between even/odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest neighbor pseudospin correlations change discontinuosly and indicate divergent correlation length at the first order quantum phase transition. At this transition one finds the disordered ground state of the compass model with high degeneracy 2×2N/22\times 2^{N/2}2×2N/2 in the limit of N→∞N\to\inftyN→∞.
We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions ${\ensuremath{\sigma}}_{i}^{z}{\ensuremath{\sigma}}_{i+1}^{z}$ and ${\ensuremath{\sigma}}_{i}^{x}{\ensuremath{\sigma}}_{i+1}^{x}$, alternating between even and/or odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest-neighbor pseudospin correlations change discontinuously and indicate divergent correlation length at the first-order quantum phase transition. At this transition, one finds the disordered ground state of the compass model with high degeneracy $2\ifmmode\times\else\texttimes\fi{}{2}^{N∕2}$ in the limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudo-spin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudo-spin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse field only emerges at zero field and is of the second-order. Several critical exponents obtained by finite size scaling analysis are the same as those in the 1D transverse field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.
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