相关论文: Exact dimer ground states for a continuous family …
We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and three-site $J_3$ interactions using the time-dependent density matrix renormalization group…
We have found the exact groundstate for a large class of antiferromagnetic spin-1 models with nearest-neighbour interactions on a linear chain. All groundstate properties can be calculated. The groundstate is determined as a matrix product…
We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly degenerate ground states even for finite system…
We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximate…
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground…
The spin-$1$ orthogonal dimer chain is investigated using the Density Matrix Renormalization Group (DMRG) algorithm. A transformation to a basis that uses the local eigenstates of the orthogonal dimers, while retaining the local spin states…
We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the $S=1/2$ chain…
We present a condition in which the dimer-monomer state is exactly the ground state of an extended diamond chain with spin magnitude 1/2. The Hamiltonian of the extended diamond chain includes next-nearest-neighbor exchange interactions and…
Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (S_{i-1} S_i)(S_i S_{i+1}) + H.c., we use density-matrix renormalization group…
We derive the exact ground space of a family of spin-1/2 Heisenberg chains with uniaxial exchange anisotropy (XXZ) and interactions between nearest and next-nearest-neighbor spins. The Hamiltonian family, H(Q), is parametrized by a single…
We study the simple Hamiltonian, $H=-K(S_{1z}^2 +S_{2z}^2)+ \lambda\vec S_1\cdot\vec S_2$, of two, large, coupled spins which are taken equal, each of total spin $s$ with $\lambda$ the exchange coupling constant. The exact ground state of…
We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet…
Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum…
We perform a systematic DMRG investigation of the two natural spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain, the spin-1 $J_1-J_2$ Heisenberg chain, where $J_2$ is a next-nearest neighbor Heisenberg coupling, and the spin-1…
We construct a new spin-1 model on a chain. Its ground state is determined exactly which is three-fold degenerate by breaking translational invariance. Thus we have trimerization. Excited states cannot be obtained exactly, but we determine…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. For the complete family of parent Hamiltonians with a ground state…
We construct the family of spin chain Hamiltonians, which have affine quantum group symmetry. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to affine…