Quantum phase diagram of spin-1 
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 Heisenberg model on the square lattice: An infinite projected entangled-pair state and density matrix renormalization group study

Haghshenas, Reza; Lan, Wu; Gong, Shou-Shu

doi:10.1103/physrevb.97.184436

Cited by 24 publications

(23 citation statements)

References 65 publications

(83 reference statements)

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“…This mapping suggests a string-VBS order at the highly frustrated regime of SL, which is in agreement with the results of COA [29]. It is worth mentioning that the TFI model could represent the large easy-axis anisotropic limit of the antiferromagnetic J 1 − J 2 Heisenberg model, where the true nature of a non-magnetic (VBS) phase is still under debate on SL [32][33][34][35][36][37][38][39] . Our results would be useful for further investigations in the latter model.…”

Section: Introductionsupporting

confidence: 88%

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

2019

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We investigate the ground-state phase diagram of the frustrated transverse field Ising (TFI) model on the checkerboard lattice (CL), which consists of Néel, collinear, quantum paramagnet and plaquette-valence bond solid (VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network (TTN) ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region (J2 = J1), we observe a second order phase transition from plaquette-VBS state to paramagnet phase at the critical magnetic field, Γc = 0.28, with the associated critical exponents ν = 1 and γ ≃ 0.4, which are obtained within the finite size scaling analysis on different lattice sizes N = 4 × 4, 6 × 6, 8 × 8. The stability of plaquette-VBS phase at low magnetic fields is examined by spin-spin correlation function, which verifies the presence of plaquette-VBS at J2 = J1 and rules out the existence of a Néel phase. In addition, our numerical results suggest that the transition from Néel (for J2 < J1) to plaquette-VBS phase is a deconfined phase transition. Moreover, we introduce a mapping, which renders the low-energy effective theory of TFI on CL to be the same model on J1 − J2 square lattice (SL). We show that the plaquette-VBS phase of the highly frustrated point J2 = J1 on CL is mapped to the emergent string-VBS phase on SL at J2 = 0.5J1.

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Section: Introductionsupporting

confidence: 88%

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

2019

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“…On cooling, the data exhibit a broad hump between 40 and 50K due to phonons followed by a steep rise at low temperatures caused by single-ion anisotropy. To extract estimates of the anisotropy parameters it is necessary to fit the data below 18K to the sum of a Debye phonon mode (see footnote 15) and the magnetic term given in equation (6). The resulting fit is displayed as a solid red line in the figure and is seen to compare well with the data at low temperatures.…”

Section: Thermodynamic Measurementsmentioning

confidence: 93%

“…The proximity of lattice and magnetic contributions to the heat capacity mean that dealing with each separately is not possible. Instead we fit the data to a model C/T=C latt /T+C mag /T, where C latt approximates the lattice contribution using a model with one Debye and three Einstein phonon modes (see footnote 15) [34], and C mag is given in equation (6). The fit is shown in the figure as a solid red line and is seen to account well for the data across the whole temperature range.…”

Section: Thermodynamic Measurementsmentioning

confidence: 94%

“…Of particular relevance here are quasi-one-dimensional and quasi-two-dimensional systems based on S=1 magnetic moments, which inspire a great deal of contemporary theoretical attention (e.g. [1][2][3][4][5][6][7][8]) and are predicted to display vibrant phase diagrams arising from competing interactions and their interplay with singleion anisotropy. These diagrams encompass quantum critical points [1,2], nematic and supersolid states [5,9,10], as well as topologically interesting gapped and quantum paramagnetic phases [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Determining the anisotropy and exchange parameters of polycrystalline spin-1 magnets

Blackmore¹,

Brambleby²,

Lancaster³

et al. 2019

New J. Phys.

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Although low-dimensional S=1 antiferromagnets remain of great interest, difficulty in obtaining highquality single crystals of the newest materials hinders experimental research in this area. Polycrystalline samples are more readily produced, but there are inherent problems in extracting the magnetic properties of anisotropic systems from powder data. Following a discussion of the effect of powder-averaging on various measurement techniques, we present a methodology to overcome this issue using thermodynamic measurements. In particular we focus on whether it is possible to characterise the magnetic properties of polycrystalline, anisotropic samples using readily available laboratory equipment. We test the efficacy of our method using the magnets [Ni(H 2 O) 2 (3,5-lutidine) 4 ](BF 4 ) 2 and Ni(H 2 O) 2 (acetate) 2 (4-picoline) 2 , which have negligible exchange interactions, as well as the antiferromagnet [Ni(H 2 O) 2 (pyrazine) 2 ](BF 4 ) 2 , and show that we are able to extract the anisotropy parameters in each case. The results obtained from the thermodynamic measurements are checked against electron-spin resonance and neutron diffraction. We also present a density functional method, which incorporates spin-orbit coupling to estimate the size of the anisotropy in [Ni(H 2 O) 2 (pyrazine) 2 ](BF 4 ) 2 .

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“…The only essential parameter which controls the accuracy of the ansatz is the so-called bond dimension D. In order to obtain highly accurate results, one should use a novel optimization scheme to access large bond dimension and to perform reliable bond-dimension scaling. iPEPS has been shown successful to study challenging problems of interacting fermions (including t-J and Hubbard models) [41][42][43] and frus-trated spin systems [44][45][46][47][48][49] . Besides model simulation, PEPS can also be constructed to strictly describe novel quantum states.…”

Section: Introductionmentioning

confidence: 99%

Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice

Haghshenas

Gong

2019

Phys. Rev. B

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We study the antiferromagnetic kagome Heisenberg model with additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of optimization algorithm in the framework of the single-layer tensor network based on the corner-transfer matrix technique. Our benchmark based on the full-update algorithm shows that the single-layer algorithm is stable, which leads to the same level of accuracy as the double-layer ansatz but with much less computation time. We further apply this algorithm to study the nature of the kagome Heisenberg model with a scalar-chiral interaction by computing the bond dimension scaling of magnetization, bond energy difference, chiral order parameter and correlation length. In particular, we find that for strong chiral coupling the correlation length, which is extracted from the transfer matrix, saturates to a finite value for large bond dimension, representing a gapped spin-liquid state. Further comparison with density matrix renormalization group results supports that our iPEPS faithfully represents the time-reversal symmetry breaking chiral state. Our iPEPS simulation results shed new light on constructing PEPS for describing gapped chiral topological states. PACS numbers: 75.40.Mg, 75.10.Jm, 75.10.Kt, 02.70.-c arXiv:1812.11436v3 [cond-mat.str-el] 23 May 2019 J ch EiPEPS m ∆Tx−y Hc J ch = 0.5 −0.4768 0.004 0.004 0.172 J ch = 2.0 −0.6889 0.006 0.002 0.231 J ch = ∞ −0.1715 0.009 0.0005 0.254

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Quantum phase diagram of spin-1 J1−J2 Heisenberg model on the square lattice: An infinite projected entangled-pair state and density matrix renormalization group study

Cited by 24 publications

References 65 publications

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

Determining the anisotropy and exchange parameters of polycrystalline spin-1 magnets

Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice

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