In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice --- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as 1/(NL), and not as 1/N or 1/L typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length L, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, L-1. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length 2L.
Motivated to elucidate the nature of quantum phases and their criticality when entangled with a correlated quantum bath, we study interacting bosons on a "comb lattice"-a one-dimensional backbone (system) coupled at its sites to otherwise independent one-dimensional "teeth" chains (bath). We map out the corresponding phase diagram, detailing the nature of the phases and phase transitions. Controlled by the backbone and teeth hopping amplitudes, short-range interactions, and chemical potential, phases include a Mott insulator, backbone, and teeth Luttinger liquids and the long-range ordered incoherent superfluid. We explore their properties and potential realizations in condensed matter and cold-atom experiments and simulations.
The prohibition of finite-temperature phase transition in one-dimensional (1D) Ising models and 1D/2D quantum Heisenberg models with short-range interactions fundamentally constrains the application potentials of low-dimensional magnetic materials. Recently, ultranarrow phase crossover (UNPC), which can approach a transition at a desirable finite temperature
T0 arbitrarily closely, was discovered in 1D decorated Ising chains and ladders. Here we present a theoretical study of similarly decorated, yet much more challenging, quantum Heisenberg ferrimagnets in a magnetic field, which features ferromagnetic backbone exchange
J, antiferromagnetic site-decoration coupling
JAF, and different magnetic moments for the backbone and decorating spins
μaSa<μbSb. We exactly solved the model in the large
J limit -- as a central-macrospin model -- and found two finite-temperature second-order transitions; just above
Tc2 a ``half-ice, half-fire'' regime appears. Finite-
J weak-field results follow from an effective-field mapping, suggesting the emergence of UNPC at finite
T0 in 2D square lattices thanks to its exponentially strong initial magnetic susceptibility
χ0∝e4πSa2J/T0, though less likely in 1D chains where
χ0∝J/T0. These results may shed light on new technological applications of low-dimensional quantum spin systems and attract experimental and computational tests.
The zero-temperature phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N)$ antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general
N. A fully gapped
SU(N) valence bond solid made of
N sites is formed above a critical value of
J2/J1 for all
N. We find that the extension of this
N-merized phase for larger values of
J2 strongly depends on the parity of
N. For even
N, the phase smoothly interpolates to the large
J2 regime where the model can be viewed as a zigzag
SU(N) two-leg spin ladder. The phase exhibits both a
N-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the
N-merized phase with odd
N has only a finite extent with no incommensuration. A gapless phase in the
SU(N)1 universality class is stabilized for larger
J2 that stems from the existence of a massless renormalization group flow from
SU(N)2 to
SU(N)1 conformal field theories when
N is odd.
By a semianalytical Bethe ansatz method and a
T-matrix approach we study the scattering of a spinon, the elementary quantum many-body topological excitation in the one-dimensional (1D) Heisenberg model, by local and phonon potentials. In particular, we contrast the scattering of a spinon to that of a free spinless fermion in the XY model to highlight the effect of strong correlations. For the one-spinon scattering in an odd-site chain, we find regular behavior of the scattering coefficients. In contrast, in an even-site chain there is a transfer of transmission probability between the two spinon branches that grows exponentially with system size. We link the exponent of the exponential behavior to the dressed charge that characterizes the critical properties of the 1D Heisenberg model, an interplay of topological and critical properties. The aim of this study is a microscopic understanding of spinon scattering by impurities, barriers, or phonons, modeled as prototype potentials, an input in the analysis of quantum spin transport experiments.
Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits.
Abstract The quantum Gaussian phase transition is investigated for the infinite spin-1 bond-alternative Heisenberg model in one spatial dimension. By using a tensor network representation with an infinite matrix product state approach, the ground state energy, bipartite entanglement entropy, non-local string order, and fidelity per lattice site are calculated to characterize the phase transition. At the quantum phase transition point, the scaling behavior of various physical observables with respect to the finite truncation dimension are discussed for the ground state wavefunctions. In addition, the central charge is extracted from the finite entanglement entropies and the finite correlation lengths. Furthermore, the various critical exponents of the string order are calculated. The characteristic critical exponents and the central charge determine the universality class of the phase transition.