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Acta Physica Sinica

INSULATOR-METAL TRANSITION OF THE 2-D HALF-FILLED HUBBARD MODEL AT FINITE-TEMPERATURES

CHHN FENG, Ying He-Ping, Tiefeng Xu, Wenzhu Li

Published Jan 1, 1994• 0 citations
Publisher

Abstract

摘要 二维半充满条件下的Ｈｕｂｂａｒｄ模型，在有限温度下，是否经历一绝缘体—金属相变？在现有的文献中，这一直是一个有争议而又重要的问题。本文采用巨正则量子Ｍｏｎｔｅ Ｃａｒｌｏ方法，计算了二维半充满条件下Ｈｕｂｂａｒｄ模型的比热和电导率。对不同的库仑排斥势Ｕ（２ｔ－８ｔ），比热曲线在高温区出现一个峰，同时电导率在相应温区呈现一突然上升。因此，计算结果支持存在这样一个相变。 Abstract In the present paper, we attempt to attack the problem of the existence of insulator-metal transition at finite temperature for a 2 dimensional half-filled Hubbard half-filled model. we used the grand Canonical quantum Monte Carlo method to caculate the electrical conductivity and the specific heac of the system. A peak on the specific heat vs temperature curve in high temperature region is observed, and the electrical conductivity curves show a sudden rise in the same temperature region. Thus, our results support that there exists a transition. 作者及机构信息 陈锋, 应和平, 徐铁锋, 李文铸 1. 浙江大学物理系 基金项目: 国家自然科学基金及浙江省自然科学基金资助的课题. Authors and contacts CHHN FENG, YING HE-PING, XU TIE-FENG, LI WEN-ZHU 1. 浙江大学物理系 参考文献 施引文献

DOI
10.7498/aps.43.1672

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摘要 二维半充满条件下的Ｈｕｂｂａｒｄ模型，在有限温度下，是否经历一绝缘体—金属相变？在现有的文献中，这一直是一个有争议而又重要的问题。本文采用巨正则量子Ｍｏｎｔｅ Ｃａｒｌｏ方法，计算了二维半充满条件下Ｈｕｂｂａｒｄ模型的比热和电导率。对不同的库仑排斥势Ｕ（２ｔ－８ｔ），比热曲线在高温区出现一个峰，同时电导率在相应温区呈现一突然上升。因此，计算结果支持存在这样一个相变。 Abstract In the present paper, we attempt to attack the problem of the existence of insulator-metal transition at finite temperature for a 2 dimensional half-filled Hubbard half-filled model. we used the grand Canonical quantum Monte Carlo method to caculate the electrical conductivity and the specific heac of the system. A peak on the specific heat vs temperature curve in high temperature region is observed, and the electrical conductivity curves show a sudden rise in the same temperature region. Thus, our results support that there exists a transition. 作者及机构信息 陈锋, 应和平, 徐铁锋, 李文铸 1. 浙江大学物理系 基金项目: 国家自然科学基金及浙江省自然科学基金资助的课题. Authors and contacts CHHN FENG, YING HE-PING, XU TIE-FENG, LI WEN-ZHU 1. 浙江大学物理系 参考文献 施引文献
In the present paper,we attempt to attack the problem of the existence of insu- 1ator- metal transition at finite temperature for a 2 dimensional half- filled Hubbard half- filled model.we used the grand Canonical quantum Monte Carlo method to ca- culate the electrical conductivity and the specific heat of the system. A peak on the specific heat vs temperature curve in high temperature region is observed,and the electrical conductivity curves show a sudden rise in the same temperature region. Thus.our results support that there exists a transition.
The Quantum Monte-Carlo simulations of the two-dimensional Hubbard model are presented for the half filling. The method based on the direct-space proposed by Suzuki and al., and Hirsch and al. was used. The states generated by this method are basis states in occupation number representation built with Wannier states localised on each site of the square array. The configurations of fermions can be observed on the real 2D array. An antiferromagnetic factor is defined and calculated for each temperature. The curves of energy, specific heat, conducivity and antiferromagnetic factor are presented for different values of the repulsive coulombian on site interaction U. There is a metal-insulator transition at low temperature for small values of U. This transition corresponds with a paramagnetic-ferromagnetic first order transition. Indeed, for these interaction values, the energy curves show a gap which is a characteristic of a first order transition. An hysteresis phenomenon appears on the conductivity curves. There is a behaviour change for U/t=3.5. For the values U>3.5 there is ferromagnetic-paramagnetic change without observable effect on the energy and the specific heat. The metal-insulator transition does not exist any more, the conductivity stays very small. Isotherms of the physical quantities versus U/t show a transition which seems to be the metal-insulator Mott transition. These results allow to draw a phase diagram with two first order transition lines.
We study the metal-insulator transition of the d-dimensional Hubbard model by treating the hopping term between adjacent 1-d chains in the frame of a Clifford linearization scheme, and keeping the full model along the chains. A general equation for the critical point is worked out in terms of the correlation functions of the one-dimensional model, assuming that the transition is of the second order. The equation, which holds at any temperature, is here investigated especially at T=0, where the latter condition holds true. The solution shows the existence of an insulating ground state in any d only at half-filling for U strictly positive, as in the exact 1-d case. The transition is found to be related to a parameter reminiscent of entropy.
The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.