Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection

Fuji, Yohei

doi:10.1103/physrevb.93.104425

Cited by 37 publications

(32 citation statements)

References 100 publications

(239 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This C-P -T anomaly is the field-theoretic description of the LSM theorem involving T and the lattice symmetries, discussed in Ref. 30,31 . An interesting future perspective would be to explore such anomalies in higher dimensional spin-half systems.…”

Section: Discussionmentioning

confidence: 87%

“…In contrast the anomaly we discuss here are fundamental anomalies of the underlying system, of the LSM-type, and they involve time-reversal and parity as well as spatial translations. The implication therefore is that the C-P -T anomaly is a different kind of LSM theorem for spin chains which preserve parity, time reversal, and lattice translational symmetries 30,31 , but not necessarily the SO(3) spin symmetry.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

C−P−T anomaly matching in bosonic quantum field theory and spin chains

Sulejmanpašić

Tanizaki

2018

Phys. Rev. B

View full text Add to dashboard Cite

We consider the O(3) nonlinear sigma model with the θ-term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any θ, and enjoys the periodicity in θ → θ + 2π. At θ = 0, π it also has a charge-conjugation C-symmetry. Gauging the discrete space-time reflection symmetries is interpreted as putting the theory on the nonorientable RP 2 manifold, after which the 2π periodicity of θ and the C symmetry at θ = π are lost. We interpret this observation as a mixed 't Hooft anomaly among charge-conjugation C, parity P , and time-reversal T symmetries when θ = π. Anomaly matching implies that in this case the ground state cannot be trivially gapped, as long as C, P and T are all good symmetries of the theory. We make several consistency checks with various semi-classical regimes, and with the exactly solvable XYZ model. We interpret this anomaly as an anomaly of the corresponding spin-half chains with translational symmetry, parity and time reversal (but not involving the SO(3)-spin symmetry), requiring that the ground state is never trivially gapped, even if SO(3) spin symmetry is explicitly and completely broken. We also consider generalizations to CP N −1 models and show that the C-P -T anomaly exists for even N .

show abstract

Section: Discussionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

C−P−T anomaly matching in bosonic quantum field theory and spin chains

Sulejmanpašić

Tanizaki

2018

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…In particular, the identification of the symmetries of the VBS phases is a non-trivial matter. 28,29 The boundaries between the phases as well as the ensuing g.s. degeneracies can be established via DMRG simulations (see Appendix D): in Fig.…”

Section: Z J I Z W F F I L J W D a R K D O N X V J S = " > A A A C mentioning

confidence: 99%

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders

et al. 2019

View full text Add to dashboard Cite

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our work is that in practice they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications. Introduction:The Majorana fermion has become one of the most important fundamental quasi particles of condensed matter physics. Besides its key role as a building block in correlated quantum matter, much of this interest is motivated by perspectives in quantum information. 1-3 Majorana qubits have unique properties which make them ideal candidates for applications in, e.g., stabilizer code quantum computation. 4 Current experimental attempts to isolate and manipulate Majorana bound states (MBSs) focus on interfaces between distinct phases of symmetry protected topological (SPT) quantum matter. These material platforms have the appealing property that MBSs are protected against local perturbations by principles of topology. In practice, however, topological protection may play a lesser role than one might hope, and various obtrusive aspects of realistic quantum materials appear to challenge the isolation and manipulation of MBSs. Specifically, in topological quantum wires based on the hybrid semiconductor-superconductor platform 5 or on coupled ferromagnetic atoms, 6 all relevant scales are confined to narrow windows in energy. In this regard, proposals to realize MBSs in topological insulator nanowires 7 may offer superior solutions. However, these realizations require a high level of tuning of external parameters, notably of magnetic fields, and may be met with their own difficulties.In this Letter, we suggest an alternative hardware platform for the isolation of zero-energy MBSs. Our proposal does not engage topology. Specifically, local perturbations of the microscopic Hamiltonian may induce nonlocal correlations between the emergent Majorana quantum particles. However, we argue below that in practice this problem is less drastic than one might fear, and that the current architecture may grant a high level of effective protection. The numerical evidence provided below certainly points in this direction.The material platform we suggest is based on spin ladder materials. Their phases can be classified by combining standard Landau-Ginzburg symmetry breaking with the presence of SPT order. 8,9 We show here that combining ladders in different phases provides a systematic means to generating interface MBSs. The formal bridge between the physics of spin ladders and that of Majorana fermions is provided by a two-step mapping, first representing the spin degrees of freedom by bosons, followed by refermionization of the latter into an effective Majorana theory. 10 We will discuss how nume...

show abstract

“…Prior theoretical and numerical investigations focus on the effects of the uniaxcial anisotropy (D-term) [17][18][19][20][21][22][23][24][25][26]. The effect of rhombic anisotropy (E-term) lacks a complete theoretical understanding [27,28]; however, materials with large D/J and E/J are discovered, e.g., the S=1 Q1D chains, Sr 3 NiPtO 6 [29,30], Ni(C 2 H 8 N 2 ) 2 Ni(CN) 4 (NENC) [31], [Ni(HF 2 )(3-Clpy) 4 ]BF 4 (py=pyridine) [32, 33], and Ni(C 10 H 8 N 2 ) 2 Ni(CN) 4 ·H 2 O (NBYC) [34][35][36].…”

mentioning

confidence: 99%

Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S=1 Haldane chain

et al. 2017

View full text Add to dashboard Cite

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxialtype, D(S z ) 2 , and the rhombic-type,, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the Z2 symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the Large-Ex, Large-Ey, or Large-D phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012)], and the Haldane-Large-D critical point is obtained with an unprecedented precision, (D/J)c=0.9684713(1). Close to this critical point, a small rhombic single-ion anisotropy |E|/J ≪ 1 can destroy the Haldane phase and bring the system into a y-Néel phase. We propose that the compound [Ni(HF2)(3-Clpy)4]BF4 is a candidate system to search for the y-Néel phase.Introduction. Quantum magnetism of integer-spin chains has been attracting attention for decades. It was stimulated by the Haldane conjecture [1] that the lowest excitation in the antiferromagnetic Heisenberg model are gapped if and only if the spin S is an integer. Experimental evidences for the Haldane gap were discovered in several S=1 quasi-one dimensional (Q1D) materials, e.g., [7, 8], and [Ni(C 2 H 8 N 2 ) 2 NO 2 ]BF 4 (NENB) [9]. Due to the crystal field and the spin-orbit coupling, the microscopic effective Hamiltonian for the Q1D spin chains involves the single-ion anisotropies,

show abstract

Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection

Cited by 37 publications

References 100 publications

C−P−T anomaly matching in bosonic quantum field theory and spin chains

C−P−T anomaly matching in bosonic quantum field theory and spin chains

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders

Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S=1 Haldane chain

Contact Info

Product

Resources

About