Identification of Unentangled–Entangled Border in the Luttinger Liquid Phase

Nemati, Somayyeh; Fumani, F. Khastehdel; Mahdavifar, S.

doi:10.3390/cryst9020105

Cited by 9 publications

(4 citation statements)

References 38 publications

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“…In many correlated systems, the entanglement has been known to characterize the QPTs. [ 5,8,31–35 ] Hence, the study of entanglement in the ANNNI chain might be useful in explorations of its phase diagram. Among numerous relations suggested for measuring entanglement, the concept of entanglement of formation is one of the common quantities.…”

Section: Resultsmentioning

confidence: 99%

Quantum Critical Lines in the Ground State Phase Diagram of Spin‐1/2 Frustrated Transverse‐Field Ising Chains

2020

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This paper focuses on the ground state phase diagram of a 1D spin‐1/2 quantum Ising model with competing first and second nearest neighbour interactions known as the axial next nearest neighbour Ising model in the presence of a transverse magnetic field. Here, using quantum correlations, both numerically and analytically, some evidence is provided to clarify the identification of the ground state phase diagram. Local quantum correlations play a crucial role in detecting the critical lines either revealed or hidden by symmetry‐breaking. A non‐symmetry‐breaking disorder transition line can be identified by the first derivative of both entanglement of formation and quantum discord between nearest neighbour spins. In addition, the quantum correlations between the second neighbour spins can also be used to reveal Kosterlitz–Thouless phase transition when their interaction strength grows and becomes closer to the first nearest neighbour one. The results obtained using the Jordan–Wigner transformation confirm the accuracy of the numerical case.

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Section: Resultsmentioning

confidence: 99%

Quantum Critical Lines in the Ground State Phase Diagram of Spin‐1/2 Frustrated Transverse‐Field Ising Chains

2020

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“…Already the seminal studies unambiguously confirm that finite quantum spin, fermion or boson system may exhibit all the hallmarks of the QPTs [12][13][14][15][16]. The exact calculation of various quantum parameters, such as entanglement [17][18][19][20][21][22][23], Loschmidt echo [24,25], fidelity [26] quantum discord (QD) [27], quantum coherence [28], time-dependent quantum behaviour of a complex few spin cluster [29,30] and quantum correlations after sudden quenches [31][32][33] has been successfully used to identify various QPTs using finite system studies. However, each tool has its limitations for different types of QPTs, and only a proper combination of used markers allows to get a correct description.…”

Section: Introductionmentioning

confidence: 99%

Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction

Japaridze,

Cheraghi,

Mahdavifar

2021

Preprint

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We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with spatially modulated Dzyaloshinskii-Moriya interaction in the presence of applied along with the ẑ axis alternating magnetic field. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of the magnetic field, the groundstate phase diagram of the model includes besides the ferromagnetic and gapless Luttiger-Liquid (LL) phases two gapped phases, the composite (C1) phase characterized by the coexistence of the long-range-ordered (LRO) alternating dimerization and the spin chirality patterns, and the composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. In the case of two-letter gapped phases, in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions (QPT) from a gapful phase into the gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalizations studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of the staggered component of the magnetic field vapes out the composite (C1) in favour of the composite gapped (C2) phase.

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“…In the last years, very powerful approaches based on the implementation of concepts partly borrowed from the quantum information theory 50 have been developed and intensively used to identify QCP in the various models of strongly correlated electron or spin systems 51 . In particular, the detailed analysis of various bipartite quantum correlations as the entanglement and the quantum discord (QD), calculated in the case of finite clusters, has been successfully used to solve these problems [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] .…”

Section: Introductionmentioning

confidence: 99%

Quantum correlations in the spin-1/2 Heisenberg XXZ chain with modulated Dzyaloshinskii-Moriya interaction

Fumani

Beradze

Nemati

et al. 2020

Preprint

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We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii-Moriya interaction, using the numerical Lanczos method. Recently, the ground state (GS) phase diagram of this model has been established using the bosonization approach and extensive density matrix renormalization group computations. Four quantum phases -saturated ferromagnetic (FM), Luttinger liquid (LL), and two (C1 and C2) gapped phases with composite structure of GS order, characterized by the coexistence of long-range alternating dimer, chirality and antiferromagnetic order have been identified. Here we reexamine the same problem using the exact diagonalization Lanczos method for chains up to N = 26 sites and explicitly detect positions of quantum critical points (QCP) by investigating the quantum correlations as the entanglement and the quantum discord (QD). It is shown that the entanglement quantified by concurrence and the first derivative of the QD are able to reveal besides the standard FM QCP also the Berezinskii-Kosterlitz-Thouless (BKT) phase transition point between the LL and the gapped C1 phase and the Ising type critical point separating the C1 and C2 phases.

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Identification of Unentangled–Entangled Border in the Luttinger Liquid Phase

Cited by 9 publications

References 38 publications

Quantum Critical Lines in the Ground State Phase Diagram of Spin‐1/2 Frustrated Transverse‐Field Ising Chains

Quantum Critical Lines in the Ground State Phase Diagram of Spin‐1/2 Frustrated Transverse‐Field Ising Chains

Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction

Quantum correlations in the spin-1/2 Heisenberg XXZ chain with modulated Dzyaloshinskii-Moriya interaction

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