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The Spin-analogy Solution of Energy Gap in Superconductor

Feng Xu, An Min Wang, Xiaodong Yang, Ma, X, You, H

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We propose a general computational method of quantum simulation to solve the energy-gap in superconductors by spin analogy and submatrix diagonalization. Our result is well consistent with the solution of the energy gap equation. It is essential to validate this type of quantum simulation on a quantum computer and is helpful to understand the many-body quantum theory.

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•Jan 1, 2008•30 citations
We propose a general computational method of quantum simulation to solve the energy-gap in superconductors by spin analogy and submatrix diagonalization. Our result is well consistent with the solution of the energy gap equation. It is essential to validate this type of quantum simulation on a quantum computer and is helpful to understand the many-body quantum theory.
We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2N-dimensional matrix is reduced to the polynomial problem of N-dimensional matrix. It is essential to validate this method on a real quantum computer and is helpful to understanding the many-body quantum theory.
We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2 N -dimensional matrix is reduced to the polynomial problem of N -dimensional matrix. It is essential to validate this method on a real quantum computer and is helpful to understanding the many-body quantum theory.
Estimating the eigenvalue or energy gap of a Hamiltonian HHH is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed-matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid nonvariational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental friendly for near-term quantum devices and early fault-tolerant quantum computers. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are maped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the problems of slowing down from which standard algorithms are suffering. Two-dimensional quantum spin systems are relevant for the description of the undoped anti-ferromagnetic precursor insulators of high-Tc superconductors. Presumably understanding the physics of the superconductors requires an understanding of their precursor insulators. This already is a nontrivial problem, which most likely does not allow for a complete analytic solution. Therefore it is natural to use a numerical approach to compute the properties of these materials. At present different