Emergent SU(3) Symmetry in Random Spin-1 Chains

Quito, Victor L.; Hoyos, José A.; Miranda, E.

doi:10.1103/physrevlett.115.167201

Cited by 16 publications

(52 citation statements)

References 36 publications

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“…In addition, we report that (not shown) C α av (x) oscillates with period of 3, as a consequence of the antiferromagnetic SU(3)symmetric character of the ground state. 42 As expected, we observed that both correlations are identical within the DMRG error.…”

Section: B the Disordered Bilinear-biquadratic Spin-1 Chainsupporting

confidence: 87%

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Adaptive density matrix renormalization group for disordered systems

2018

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We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach larger system sizes in the strong disorder limit by avoiding most of the metastable configurations which hinder the performance of the standard DMRG method. We benchmark our adaptive method by revisiting the random antiferromagnetic XXZ spin-1/2 chain for which we compute the randomsinglet ground-state average spin-spin correlation functions and von Neumann entanglement entropy. We then apply our method to the bilinear-biquadratic random antiferromagnetic spin-1 chain tuned to the antiferromagnet and gapless highly symmetric SU(3) point. We find the new result that the mean correlation function decays algebraically with the same universal exponent φ = 2 as the spin-1/2 chain. We then perform numerical and analytical strong-disorder renormalization-group calculations, which confirm this finding and generalize it for any highly symmetric SU(N) random-singlet state.

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Section: B the Disordered Bilinear-biquadratic Spin-1 Chainsupporting

confidence: 87%

“…We then focus on the case θ = π 4 which exhibits exact SU(3) symmetry [i.e., the Hamiltonian (7) becomes H = ∑ i J i Λ i · Λ i+1 + const] placing the system in the Baryonic RS phase. 42 In Fig. 3, we plot the arithmetic average correlations C α av (x) Eq.…”

Section: B the Disordered Bilinear-biquadratic Spin-1 Chainmentioning

confidence: 99%

Adaptive density matrix renormalization group for disordered systems

2018

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“…The random Heisenberg Antiferromagnetic spin chain is the first model where SDRG has been introduced [1]. After the various works already reviewed in [3], more recent studies include the effects of next-nearest-neighbor interaction in d = 1 [58], the case of wealkly coupled chains [59], models in dimension d = 2 [60][61][62], as well as the generalizations to various type continuous symmetry (SU (3), SU (N ), SO(N )) considered in the series of papers [63][64][65][66][67], where different types of random singlet phases are identified via SDRG and the low-energy behaviour is controlled by infinite disorder fixed points.…”

Section: B Models With Continuous Symmetrymentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

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Relations between SDRG and Entanglement-Algorithms 10 VI. Localized and Many-Body-Localized Phases of quantum spin chains 11 A. RSRG-X for excited eigenstates 11 B. RSRG-t for the unitary dynamics 11 C. Non-equilibrium dynamical scaling of observables 12 D. Comparison with other RG procedures existing in the field of Many-Body-Localization 13 VII. Floquet dynamics of periodically driven chains in their localized phases 13 VIII. Open dissipative quantum spin chains 13 A. Quantum spin chains coupled to a bath of quantum oscillators 13 B. Lindblad dynamics for random quantum spin chains 14 IX. Anderson localization models 14 X. Random contact process 14 A. Strong disorder RG rules 15 B. Long range spreading 15 C. Temporal disorder 15 XI. Classical master equations 16 A. Real-space renormalization for random walks in random media 16 B. RG in configuration-space for the dynamics of classical many-body models 16 XII. Random classical oscillators 17 A. Random elastic networks 17 B. Synchronisation of interacting non-linear dissipative classical oscillators 17 XIII. Other classical models 17 A. Equilibrium properties of random systems 17 B. Extremes of stochastic processes 18 XIV. Conclusion 18

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“…Randomness has been shown to modify the characteristics of phase transi- * These two authors contributed equally. tions [34,35], as well as transition a spin system from one universality class to another [36,37] and is integral to the emergence of interesting phases such as the Griffiths and random singlet phases (RSPs) [38][39][40]. Recently a lot of attention has been devoted to the mechanism of manybody localisation in 1D and 2D systems [41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Schmidt gap in random spin chains

2018

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We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two paradigmatic models: the spin-1/2 random transverse field Ising model, solved exactly, and the spin-1 random Heisenberg model, simulated using the density matrix renormalization group. In both cases we analyze the mean Schmidt gap, defined as the difference between the two largest eigenvalues of the reduced density matrix of one of the two partitions, averaged over many disorder realizations. We find that the Schmidt gap detects the critical point very well and scales with universal critical exponents.

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Emergent SU(3) Symmetry in Random Spin-1 Chains

Cited by 16 publications

References 36 publications

Adaptive density matrix renormalization group for disordered systems

Adaptive density matrix renormalization group for disordered systems

Strong disorder RG approach – a short review of recent developments

Schmidt gap in random spin chains

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