A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1) symmetry which is known from previous studies to mix up antiferromagnetic order parameter with that of the
p-type nematic, we find an emergent U(1) symmetry which mixes order parameters dual to the above. On the basis of the field-theoretical and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g., the bosonic $t\text{\ensuremath{-}}J$ model) is also discussed.
We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.
We present the phase diagram of the
S=1/2 Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.
We investigate a two-leg Heisenberg spin ladder with cyclic four-spin exchange by exploiting a newly-developed tensor network algorithm. The algorithm allows to efficiently compute the ground-state fidelity per lattice site, which enables us to establish the ground-state phase diagram for quantum lattice many-body systems. The latter is based on the observation that, for an infinite-size system, any singularity on a ground-state fidelity surface characterizes a critical point, at which the system undergoes a phase transition. For the two-leg Heisenberg spin-1/2 ladder with cyclic four-spin exchange, six different phases are identified: the ferromagnetic phase, the rung singlet phase, the staggered dimer phase, the scalar chirality phase, the dominant vector chirality region, and the dominant collinear spin region. Our findings are in a good agreement with the previous studies from the exact diagonalization and the density-matrix renormalization group.
The spin-1/2 transverse field two-leg Ising ladder with nearest-neighbor exchange and plaquette four-spin interaction
J4 is studied analytically and numerically with the density matrix renormalization group approach. The quantum phase diagram in the transverse field
B versus
J4 plane has been obtained. There are three different phases: a paramagnetic (PM) phase for high values of the transverse field and, for low values of
B, a ferromagnetic (FM) ordered phase for small
J4, and a dimerized-rung (DR) phase for large negative values of
J4. All phases are separated by quantum phase transition lines meeting at a multicritical point. The critical lines have been obtained by exploring the entanglement entropy. The results show that along the critical lines the central charge is
c=1/2, while at the multicritical point one has
c=1. The scaling dimension of the energy operator is ${X}_{\ensuremath{\epsilon}}=1$, in agreement with the universality class of the critical behavior of the quantum Ising chain. An effective field theory for the multicritical point is also discussed. The FM and the DR order parameters have also been computed and we found a region where the FM and the DR phases coexist.
We present a field-theory analysis of a model of two
SU(2n)-invariant magnetic chains coupled by a generic interaction preserving time-reversal and inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature phase diagram of such two-leg spin ladder does not contain topological phases. Only generalized valence bond solid phases are stabilized when
n>1 with different wave vectors and ground-state degeneracies. In particular, we find a phase which is made of a cluster of
2n spins put in an
SU(2n) singlet state. For
n=3, this cluster phase is relevant to
173Yb ultracold atoms, with an emergent SU(6) symmetry, loaded in a double-well optical lattice.