| Vladimir Korepin | |
|---|---|
| Born | 6 February 1951 Russia |
| Nationality | Russian- American |
| Fields | Physics, Mathematics |
| Institutions | State University of New York |
| Alma mater | Saint Petersburg State University |
| Doctoral advisor | Ludwig Faddeev |
| Notable students | Samson Shatashvilli [1]; Fabian Essler [2]; Vitaly Tarasov [3] |
Vladimir Korepin (born in 1951) is a Russian-American physicist and mathematician. He is a professor at the C. N. Yang Institute of Theoretical Physics of the State University of New York at Stony Brook. Korepin has notable results in several areas and has published about 187 papers in theoretical and mathematical physics.
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Korepin completed his undergraduate study at Saint Petersburg State University, graduating with a diploma in theoretical physics in 1974.[1] In that same year he was employed by the Mathematical Institute of Academy of Sciences of Russia. He complted his graduate and postdoctoral studies in this Institute and worked there until 1989. Korepin obtained his PhD degree in mathematical physics in 1977 from the Mathematical Institute of the Academy of Sciences of Russia in Moscow. His scientific adviser was Ludwig Faddeev. In 1985, he got a degree of doctor of sciences in mathematical physics from the Council of Ministers of the Russian Federation.
One of Korepin's results in quantum gravity (cancellation of ultra-violet infinities in one loop gravity on mass shell) was cited in the Feynman lectures on gravitation by Richard Feynman, edited by B. Hatfield, R. B. Morinigo and W. G. Wagner.[2][3]
His papers on 1D Hubbard model (the central model of strongly correlated electrons) has citations in condensed matter physics. He has written a textbook with F. H. L. Essler,H. Frahm, F. Goehmann and A. Kluemper on the exact solution of the Hubbard model in one dimension.[4]
Korepin has contributed results in 1D Bose gas with a delta potential interactions. He has written a book [with Bogoliubov and Izergin] for Cambridge University Press in 1993 about the Bose gases with delta interactions.[5] The book can also be used as a textbook on quantum inverse scattering method and the algebraic Bethe ansatz.
Korepin presented a solution of the massive Thirring model in one space and one time dimension using Bethe ansatz; in particular, the exact calculation of the mass spectrum and the scattering matrix. The paper with this solution was first published in Russian in 1979,[6] and was translated into English in Theoretical and Mathematical Physics. [7]
He has also made a semiclassical calculation and one loop corrections to the mass of solitons (including bound states) and the scattering matrix (in reflectionless cases scattering matrices were obtained exactly). The main example used in his published work is the sine-Gordon model.[8]
He discovered, in collaboration with Anatoly Izergin, the 19-vertex model (sometimes called the Izergin-Korepin model).[9]
In 1993 Korepin together with A.R.Its, A.G.Izergin and N.A.Slavnov calculated space, time and temperature dependent correlation functions in isotropic version of the XY spin chain using the Heisenberg model. The correlation function decays exponentially with time and space separation. The rate of exponential decay is evaluated explicitly.[10]
In 1982, Korepin introduced domain wall boundary conditions for the six vertex model, published in Communications in Mathematical Physics.[11] The result plays a role in diverse fields of mathematics such as algebraic combinatorics, Alternating sign matrixes, domino tiling, Young diagrams and plane partitions. In the same paper the determinant formula was proved for the square of the norm of the Bethe ansatz wave function. It can be represented as a determinant of linearized system of Bethe equations. It can also be represented as a matrix determinant of second derivatives of the Yang action.
The so called "Quantum Determinant" was discovered in 1981 by A.G. Izergin and V.E. Korepin.[12] It is the center of the Yang–Baxter algebra.
The study of differential equations for quantum correlation functions led to the discovery of a special class of Fredholm integral operators. Now they are referred to as completely integrable integral operators. [13] They have multiple applications not only to quantum exactly solvable models, but also to random matrices and algebraic combinatorics.
Vladimir Korepin has produced important results in the evaluation of the entanglement entropy of different dynamical models, such as interacting spins, Bose gases, and the Hubbard model.[14] He considered models with a unique ground states, so that the entropy of the whole ground state is zero. The ground state is partitioned into two spatially separated parts: the block and the environment. He calculated the entropy of the block as a function of its size and other physical parameters. In a series of articles, [15][16][17][18][19] Korepin was the first to compute the analytic formula for the entanglement entropy of the XX (isotropic) and XY Heisenberg models. He used Toeplitz Determinants and Fisher-Hartwig Formula for the calculation. In the Valence-Bond-Solid states (which is the ground state of the Affleck-Kennedy-Lieb-Tasaki model of interacting spins), Korepin evaluated the entanglement entropy and studied the reduced density matrix.[20][21] He also worked on quantum search algorithms with Lov Grover.[22][23] Many of his publications on entanglement and quantum algorithms can be found on arxiv.org.[24]
In May 2003, Korepin helped organize a conference on quantum and reversible computations in Stony Brook.[25] Another conference is scheduled for November 15-18th 2010, entitled the "Simons Conference on New Trends in Quantum Computation".[26]
In 1996 Korepin was elected fellow of the American Physical Society.[27] He is also a fellow of the International Association of Mathematical Physics and the Institute of Physics.[27] He is an editor of Reviews in Mathematical Physics, the International Journal of Modern Physics and Theoretical and Mathematical Physics. His 60's birthday was celebrated by Institute of Advanced Studies in Singapore in 2011[28].