Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0911.1334 · Journal of Physics Conference Series

Analysis of the magnetic response of the edge-sharing chain cuprate Li2CuO2within TMRG

Evgeny A. Plekhanov, Adolfo Avella, Ferdinando Mancini

Published Jan 1, 2010• 1 citation
arXivHTMLPDF

Abstract

It is widely accepted that the low-energy physics in edge-sharing cuprate materials has one-dimensional (1D) character. The relevant model to study such systems is believed to be the 1D extended Heisenberg model with ferromagnetic nearest-neighbor (NN) interaction and antiferromagnetic next-nearest-neighbor one. Thus far, however, theoretical studies of such materials have been confined to the case of isotropic interactions. In the present work, we compare the spin susceptibility of the 1D extended Heisenberg model with anisotropy in the NN channel, obtained by means of the Transfer Matrix Renormalization Group method, with that of the edge-sharing chain cuprate Li 2 CuO 2 .

DOI
10.1088/1742-6596/200/2/022047

Related papers

Thermodynamics of the frustrated ferromagnetic spin-1/2 Heisenberg chain

Johannes Richter, M. Härtel, Dieter Ihle +1 more

Abstract. We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic nextnearest-neighbor bonds J2> 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T −2 at J2 < |J1|/4 to χ ∝ T −3/2 at the quantum-critical point J2 = |J1|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat Cv(T) for J2 � |J1|/8, indicating its strong influence on the low-energy spectrum. Introduction: In low-dimensional frustrated quantum magnets thermal and quantum fluctuations strongly influence the low-temperature physics [1,2]. Special attention has been paid to one-dimensional (1D) J1-J2 quantum Heisenberg magnets, see Ref. [3] and references therein. Recent experimental studies have shown that edge-shared chain cuprates, such as LiVCuO4, Li(Na)Cu2O2, Li2ZrCuO4, and Li2CuO2 [4–13], represent a family of quantum magnets for

•Nov 21, 2012•4 citations

Comparison between disordered quantum spin- 12 chains

Carlos Alberto Lamas, D. C. Cabra, Marcelo D. Grynberg +1 more

We study the magnetic properties of two types of one-dimensional $XX$ spin-$\frac{1}{2}$ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.

arXiv:cond-mat/0607387•Physical Review B•Dec 27, 2006•12 citations

Zigzag spin chains with antiferromagnetic-ferromagnetic interactions

Hantao Lu, Y. J. Wang, Shaojin Qin +1 more

Properties of the zigzag spin chains with various nearest-neighbor and next-nearest-neighbor interactions are studied by making use of the transfer-matrix renormalization group method. Thermodynamic quantities of the systems (temperature dependence of the susceptibility and the specific heat), as well as the field dependence of the magnetization are analyzed numerically with a high accuracy in the thermodynamic limit. The results have been compared with the recent experimental data on Rb$_2$Cu$_{2}$Mo$_{3}$O$_{12}$.

arXiv:cond-mat/0603519•Mar 20, 2006•0 citations

Susceptibility behavior of CuGeO3: Comparison between experiment and the quantum transfer-matrix approach

G. Kamieniarz, M. Bieliński, Jean‐Pierre Renard

Thermodynamical properties of the one-dimensional $S=1/2$ Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions are studied by the numerically exact quantum transfer-matrix method and the results are applied to ${\mathrm{CuGeO}}_{3}.$ The Suzuki-Trotter formula is used to obtain a classical system with spin $\ensuremath{\sigma}=3/2$ and effective interactions between nearest neighbors only. The magnetic susceptibility curve is calculated and compared with experimental results in a wide temperature range, revealing the presence of frustration in the model proposed for ${\mathrm{CuGeO}}_{3}.$ Temperature dependence of the dimerization parameter below the spin-Peierls transition point is also estimated.

Physical review. B, Condensed matter•Dec 1, 1999•11 citations

Ground-State Properties of the t–J Model for the CuO Double-Chain Structure

Tatsuya Kaneko, Satoshi Ejima, K. Sugimoto +1 more

We investigate the ground-state properties of a correlated model for the double-chain structure in cuprates. We consider the $t$-$J$ model, in which the nearest-neighbor spin interaction $J_1$ is smaller than the next-nearest-neighbor interaction $J_2$ corresponding to the CuO double-chain structure. We vary $J_1$ from antiferromagnetic to ferromagnetic values and calculate the correlation functions including the superconducting pair correlation function. Employing the density-matrix renormalization group method, we show that the ground state for antiferromagnetic $J_1$ exhibits the hallmarks of the Luther-Emery liquid phase, in which the spin-singlet pair and charge-density-wave correlations exhibit power-law decays against distance, and the spin correlation function decays exponentially. Its signatures are gradually dismissed as $J_1$ approaches the ferromagnetic regime. Our findings suggest that the antiferromagnetic double-chain structure without ferromagnetic bonds is favorable for superconductivity.

arXiv:2407.16325•Journal of the Physical Society of Japan•Jul 23, 2024•3 citations

Anisotropic spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic interactions

Jay D. Mancini, Janice D. Prie, William J. Massano

Using a reduced Lanczos scheme, we evaluate the ground-state energy and all two-particle correlation functions of a one-dimensional Heisenberg spin-1/2 model with antiferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. The effects of anisotropy are also considered.

Physical review. B, Condensed matter•Mar 1, 1994•7 citations
It is widely accepted that the low-energy physics in edge-sharing cuprate materials has one-dimensional (1D) character. The relevant model to study such systems is believed to be the 1D extended Heisenberg model with ferromagnetic nearest-neighbor (NN) interaction and antiferromagnetic next-nearest-neighbor one. Thus far, however, theoretical studies of such materials have been confined to the case of isotropic interactions. In the present work, we compare the spin susceptibility of the 1D extended Heisenberg model with anisotropy in the NN channel, obtained by means of the Transfer Matrix Renormalization Group method, with that of the edge-sharing chain cuprate Li 2 CuO 2 .
Abstract. We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic nextnearest-neighbor bonds J2> 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T −2 at J2 < |J1|/4 to χ ∝ T −3/2 at the quantum-critical point J2 = |J1|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat Cv(T) for J2 � |J1|/8, indicating its strong influence on the low-energy spectrum. Introduction: In low-dimensional frustrated quantum magnets thermal and quantum fluctuations strongly influence the low-temperature physics [1,2]. Special attention has been paid to one-dimensional (1D) J1-J2 quantum Heisenberg magnets, see Ref. [3] and references therein. Recent experimental studies have shown that edge-shared chain cuprates, such as LiVCuO4, Li(Na)Cu2O2, Li2ZrCuO4, and Li2CuO2 [4–13], represent a family of quantum magnets for
We study the magnetic properties of two types of one-dimensional XXXXXX spin-12\frac{1}{2}21​ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.
Properties of the zigzag spin chains with various nearest-neighbor and next-nearest-neighbor interactions are studied by making use of the transfer-matrix renormalization group method. Thermodynamic quantities of the systems (temperature dependence of the susceptibility and the specific heat), as well as the field dependence of the magnetization are analyzed numerically with a high accuracy in the thermodynamic limit. The results have been compared with the recent experimental data on Rb2_22​Cu2_{2}2​Mo3_{3}3​O12_{12}12​.
Thermodynamical properties of the one-dimensional S=1/2S=1/2S=1/2 Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions are studied by the numerically exact quantum transfer-matrix method and the results are applied to CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​. The Suzuki-Trotter formula is used to obtain a classical system with spin $\ensuremath{\sigma}=3/2$ and effective interactions between nearest neighbors only. The magnetic susceptibility curve is calculated and compared with experimental results in a wide temperature range, revealing the presence of frustration in the model proposed for CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​. Temperature dependence of the dimerization parameter below the spin-Peierls transition point is also estimated.
We investigate the ground-state properties of a correlated model for the double-chain structure in cuprates. We consider the ttt-JJJ model, in which the nearest-neighbor spin interaction J1J_1J1​ is smaller than the next-nearest-neighbor interaction J2J_2J2​ corresponding to the CuO double-chain structure. We vary J1J_1J1​ from antiferromagnetic to ferromagnetic values and calculate the correlation functions including the superconducting pair correlation function. Employing the density-matrix renormalization group method, we show that the ground state for antiferromagnetic J1J_1J1​ exhibits the hallmarks of the Luther-Emery liquid phase, in which the spin-singlet pair and charge-density-wave correlations exhibit power-law decays against distance, and the spin correlation function decays exponentially. Its signatures are gradually dismissed as J1J_1J1​ approaches the ferromagnetic regime. Our findings suggest that the antiferromagnetic double-chain structure without ferromagnetic bonds is favorable for superconductivity.