References#
Exact diagonalization and numerical methods#
H. Q. Lin, J. E. Gubernatis, H. Gould, and J. Tobochnik, “Exact Diagonalization Methods for Quantum Systems,” Computers in Physics 7, 400-407 (1993). doi:10.1063/1.4823192
A. W. Sandvik, “Computational Studies of Quantum Spin Systems,” AIP Conference Proceedings 1297, 135-338 (2010). arXiv:1101.3281
R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM (1998). doi:10.1137/1.9780898719628
P. Virtanen et al., “SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,” Nature Methods 17, 261-272 (2020). doi:10.1038/s41592-019-0686-2
C. R. Harris et al., “Array programming with NumPy,” Nature 585, 357-362 (2020). doi:10.1038/s41586-020-2649-2
Fermionic reference models#
D. J. Carrascal, J. Ferrer, J. C. Smith, and K. Burke, “The Hubbard dimer: a density functional case study of a many-body problem,” Journal of Physics: Condensed Matter 27, 393001 (2015). doi:10.1088/0953-8984/27/39/393001
E. H. Lieb and F. Y. Wu, “Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension,” Physical Review Letters 20, 1445 (1968). doi:10.1103/PhysRevLett.20.1445
M. Nakamura, “Mechanism of CDW-SDW Transition in One Dimension,” Journal of the Physical Society of Japan 68, 3123-3126 (1999). doi:10.1143/JPSJ.68.3123
P. Sengupta, A. W. Sandvik, and D. K. Campbell, “Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model,” Physical Review B 65, 155113 (2002). doi:10.1103/PhysRevB.65.155113
E. Jeckelmann, “Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model,” Physical Review Letters 89, 236401 (2002). doi:10.1103/PhysRevLett.89.236401
N. Byers and C. N. Yang, “Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders,” Physical Review Letters 7, 46 (1961). doi:10.1103/PhysRevLett.7.46
M. Büttiker, Y. Imry, and R. Landauer, “Josephson behavior in small normal one-dimensional rings,” Physics Letters A 96, 365-367 (1983). doi:10.1016/0375-9601(83)90011-7
Bosonic reference models#
D. P. Arovas and A. Auerbach, “Functional integral theories of low-dimensional quantum Heisenberg models,” Physical Review B 38, 316 (1988). doi:10.1103/PhysRevB.38.316
O. Penrose and L. Onsager, “Bose-Einstein Condensation and Liquid Helium,” Physical Review 104, 576-584 (1956). doi:10.1103/PhysRev.104.576
J. M. Zhang and R. X. Dong, “Exact diagonalization: the Bose-Hubbard model as an example,” European Journal of Physics 31, 591-602 (2010). doi:10.1088/0143-0807/31/3/016, arXiv:1102.4006
M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Physical Review B 40, 546 (1989). doi:10.1103/PhysRevB.40.546
D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold Bosonic Atoms in Optical Lattices,” Physical Review Letters 81, 3108 (1998). doi:10.1103/PhysRevLett.81.3108
G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Physical Review A 55, 4318 (1997). doi:10.1103/PhysRevA.55.4318
A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Physical Review Letters 79, 4950 (1997). doi:10.1103/PhysRevLett.79.4950
S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, pi oscillations, and macroscopic quantum self-trapping,” Physical Review A 59, 620 (1999). doi:10.1103/PhysRevA.59.620
A. Schuckert, A. Piñeiro Orioli, and J. Berges, “Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation,” Physical Review B 98, 224304 (2018). doi:10.1103/PhysRevB.98.224304