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arXiv:2012.14908 · SciPost Physics

Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

Luhang Yang, Phillip Weinberg, Adrian E. Feiguin

Published Sep 21, 2022• 10 citations
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Abstract

We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent \alpha α . Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons – bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.

DOI
10.21468/scipostphys.13.3.060

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We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent \alpha α . Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons – bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent α\alphaα. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken Neel phase at αc∼2.1\alpha_c\sim 2.1αc​∼2.1. We find evidence that the transition is second order with a dynamic critical exponent z=1z=1z=1 and ν≈1.2\nu\approx 1.2ν≈1.2. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- bound states of spinons across the legs. We obtained the momentum resolved spin dynamic structure factor numerically and found that the triplon band is well defined at high energies and adiabatically connected to the magnon dispersion. However, at low energies it emerges as the lower edge of continuum of excitations that shifts to high energies across the transition. We further discuss the possibility of deconfined criticality in this model.
We study the nature of the excitations of an antiferromagnetic (AFM) Heisenberg chain with staggered long range interactions using the time-dependent density matrix renormalization group method and by means of a multi-spinon approximation. The chain undergoes true symmetry breaking and develops long range order, transitioning from a gapless spin liquid to a gapless ordered AFM phase. The spin dynamic structure factor shows that the emergence of Néel order can be associated to the formation of bound states of spinons that become coherent magnons. The quasiparticle band leaks out from the two-spinon continuum that is pushed up to higher energies. Our physical picture is also supported by an analysis of the behavior of the excitations in real-time.
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.
We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.
We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the Néel phase with broken SU(2)-symmetry in quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. To this end, we determine high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. This is achieved by extending the method of perturbative continuous unitary transformations (pCUT) to long-range Heisenberg interactions and to the calculation of generic observables. The quantum-critical breakdown of the rung-singlet phase then allows us to determine the critical phase transition line and the entire set of critical exponents as a function of the decay exponent of the long-range interaction. We demonstrate long-range mean-field behavior as well as a non-trivial regime of continuously varying critical exponents implying the absence of deconfined criticality contrary to a recent suggestion in the literature.
We study spin-1/21/21/2 chains with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange Jr∝r−αJ_r \propto r^{-α}Jr​∝r−α and multi-spin interactions QQQ favoring a valence-bond solid (VBS) ground state. Employing quantum Monte Carlo techniques and Lanczos diagonalization, we analyze order parameters and excited-state level crossings to characterize quantum states and phase transitions in the (α,Q)(α,Q)(α,Q) plane. For weak QQQ and sufficiently slowly decaying Heisenberg interactions (small ααα), the system has a long-range-ordered antiferromagnetic (AFM) ground state, and upon increasing ααα there is a continuous transition into a quasi long-range ordered (QLRO) critical state of the type in the standard Heisenberg chain. For rapidly decaying long-range interactions, there is transition between QLRO and VBS ground states of the same kind as in the frustrated J1J_1J1​-J2J_2J2​ Heisenberg chain. Our most important finding is a direct continuous quantum phase transition between the AFM and VBS states - a close analogy to the 2D deconfined quantum-critical point. In previous 1D analogies the ordered phases both have gapped fractional excitations, and the critical point is a conventional Luttinger Liquid. In our model the excitations fractionalize upon transitioning from the AFM state, changing from spin waves to deconfined spinons. We extract critical exponents at the AFM-VBS transition and use order-parameter distributions to study emergent symmetries. We find emergent O(444) symmetry of the O(333) AFM and scalar VBS order parameters. Thus, the order parameter fluctuations exhibit the covariance of a uniaxially deformed O(444) sphere (an "elliptical" symmetry). This unusual quantum phase transition does not yet have any known field theory description, and our detailed results can serve to guide its construction. We discuss possible experimental realizations.