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Dey D, Parvej A, Das S, Saha SK, Kumar M, Ramasesha S, Soos ZG. Density matrix renormalization group (DMRG) for interacting spin chains and ladders. J CHEM SCI 2023. [DOI: 10.1007/s12039-023-02140-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/30/2023]
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Chatterjee M, Maiti D, Kumar M. Quantum Phase Diagram of a Frustrated Spin-1/2 Ferro-Antiferromagnetic Normal Ladder. Chemphyschem 2023; 24:e202200538. [PMID: 36315358 DOI: 10.1002/cphc.202200538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Revised: 10/31/2022] [Accepted: 10/31/2022] [Indexed: 12/14/2022]
Abstract
In this work, we consider a frustrated two-leg spin-1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin-1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non-collinear ferrimagnetic (NCF), m - 1 / 4 ${m - 1/4}$ , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin-1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of m - 1 / 4 ${m - 1/4}$ phase and calculate the pitch angle θ ${\left( \theta \right)}$ in the NCF phase.
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Affiliation(s)
- Monalisa Chatterjee
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata, 700106, India
| | - Debasmita Maiti
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata, 700106, India.,Department of Physics, National Tsing Hua University, Hsinchu, 300044, Taiwan
| | - Manoranjan Kumar
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata, 700106, India
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Rahaman SS, Haldar S, Kumar M. Machine learning approach to study quantum phase transitions of a frustrated one dimensional spin-1/2 system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:115603. [PMID: 36599166 DOI: 10.1088/1361-648x/acb030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 01/04/2023] [Indexed: 06/17/2023]
Abstract
Frustration-driven quantum fluctuation leads to many exotic phases in the ground state (GS) and the study of these quantum phase transitions is one of the most challenging areas of research in condensed matter physics. We study a frustrated HeisenbergJ1-J2model of spin-1/2 chain with nearest exchange interactionJ1and next nearest exchange interactionJ2using the principal component analysis (PCA) which is an unsupervised machine learning technique. In this method most probable spin configurations (MPSCs) of GS and first excited state (FES) for differentJ2/J1are used as the input in PCA to construct the covariance matrix. The 'quantified principal component'p1(J2/J1)of the largest eigenvalue of the covariance matrix is calculated and it is shown that the nature and variation ofp1(J2/J1)can accurately predict the phase transitions and degeneracies in the GS. Thep1(J2/J1)calculated from the MPSC of GS only exhibits the signature of degeneracies in the GS, whereas,p1(J2/J1)calculated from the MPSC of FES captures the gapless spin liquid (GSL)-dimer phase transition as well as all the degeneracies of the model system. We show that the jump inp1(J2/J1)of FES atJ2/J1≈0.241, indicates the GSL-dimer phase transition, whereas its kinks give the signature of the GS degeneracies. The scatter plot of the first two principal components of FES shows distinct band formation for different phases. The MPSCs are obtained by using an iterative variational method (IVM) which gives the approximate eigenvalues and eigenvectors.
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Affiliation(s)
- Sk Saniur Rahaman
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Sumit Haldar
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Manoranjan Kumar
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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Saniur Rahaman S, Sahoo S, Kumar M. Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising-Heisenberg rung interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:265801. [PMID: 33857937 DOI: 10.1088/1361-648x/abf882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 04/15/2021] [Indexed: 06/12/2023]
Abstract
We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropicS-type or discrete anisotropicσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, bothSandσ-type of spins are anti-ferromagnetically aligned with each other, two nearestSspins along the rung form an anisotropic singlet bond whereas two nearestσspins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heatCv(T), magnetic susceptibilityχ(T) and thermal entropyS(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed fromχ(T) andCv(T) curves.
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Affiliation(s)
- Sk Saniur Rahaman
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Shaon Sahoo
- Department of Physics, Indian Institute of Technology, Tirupati, India
| | - Manoranjan Kumar
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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Herbrych J, Heverhagen J, Alvarez G, Daghofer M, Moreo A, Dagotto E. Block-spiral magnetism: An exotic type of frustrated order. Proc Natl Acad Sci U S A 2020; 117:16226-16233. [PMID: 32601231 PMCID: PMC7368323 DOI: 10.1073/pnas.2001141117] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Competing interactions in quantum materials induce exotic states of matter such as frustrated magnets, an extensive field of research from both the theoretical and experimental perspectives. Here, we show that competing energy scales present in the low-dimensional orbital-selective Mott phase (OSMP) induce an exotic magnetic order, never reported before. Earlier neutron-scattering experiments on iron-based 123 ladder materials, where OSMP is relevant, already confirmed our previous theoretical prediction of block magnetism (magnetic order of the form [Formula: see text]). Now we argue that another phase can be stabilized in multiorbital Hubbard models, the block-spiral state. In this state, the magnetic islands form a spiral propagating through the chain but with the blocks maintaining their identity, namely rigidly rotating. The block-spiral state is stabilized without any apparent frustration, the common avenue to generate spiral arrangements in multiferroics. By examining the behavior of the electronic degrees of freedom, parity-breaking quasiparticles are revealed. Finally, a simple phenomenological model that accurately captures the macroscopic spin spiral arrangement is also introduced, and fingerprints for the neutron-scattering experimental detection are provided.
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Affiliation(s)
- J Herbrych
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996;
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - J Heverhagen
- Institute for Functional Matter and Quantum Technologies, University of Stuttgart, D-70550 Stuttgart, Germany
- Center for Integrated Quantum Science and Technology, University of Stuttgart, D-70550 Stuttgart, Germany
| | - G Alvarez
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831
| | - M Daghofer
- Institute for Functional Matter and Quantum Technologies, University of Stuttgart, D-70550 Stuttgart, Germany
- Center for Integrated Quantum Science and Technology, University of Stuttgart, D-70550 Stuttgart, Germany
| | - A Moreo
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
| | - E Dagotto
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
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Modeling the Neutral-Ionic Transition with Correlated Electrons Coupled to Soft Lattices and Molecules. CRYSTALS 2017. [DOI: 10.3390/cryst7050144] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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Dey D, Maiti D, Kumar M. An efficient density matrix renormalization group algorithm for chains with periodic boundary condition. PAPERS IN PHYSICS 2016. [DOI: 10.4279/pip.080006] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022] Open
Abstract
The Density Matrix Renormalization Group (DMRG) is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC) from the conventional DMRG has been a challenging job from the inception of DMRG. The recent development of the Matrix Product State (MPS) algorithm gives a new approach to find accurate results for the one dimensional PBC system. The most efficient implementation of the MPS algorithm can scale as O($p \times m^3$), where $p$ can vary from 4 to $m^2$. In this paper, we propose a new DMRG algorithm, which is very similar to the conventional DMRG and gives comparable accuracy to that of MPS. The computation effort of the new algorithm goes as O($m^3$) and the conventional DMRG code can be easily modified for the new algorithm.Received: 2 August 2016, Accepted: 12 October 2016; Edited by: K. Hallberg; DOI: http://dx.doi.org/10.4279/PIP.080006Cite as: D Dey, D Maiti, M Kumar, Papers in Physics 8, 080006 (2016)This paper, by D Dey, D Maiti, M Kumar, is licensed under the Creative Commons Attribution License 3.0.
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