Hybrid exact diagonalization and density matrix renormalization group approach to the thermodynamics of one-dimensional quantum models

Saha, Sudip Kumar; Dey, Dayasindhu; Kumar, Manoranjan; Soos, Z. G.

doi:10.1103/physrevb.99.195144

Cited by 15 publications

(24 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The color-coded line S(T, α c ) is again shifted by 0.03. The dashed line S(T, 0) is the exact [ initially linear in T , that previously served to validate the ED/DMRG method [15]. Frustration increases S(T, α c ) by about 20% above S(T, 0) at low T .…”

Section: Introductionmentioning

confidence: 92%

“…We summarize the DMRG calculations in sectors with total 0 ≤ S Z ≤ N/2 presented in detail and tested in Ref. 15. The singlet ground state is in the S Z = 0 sector.…”

Section: Dmrg and Convergencementioning

confidence: 99%

“…The thermodynamic limit χ(T, α) + 0.02 is shown as a bold red line through the points that smoothly connects to ED at high T . Convergence to χ(T, α) is from below and has been checked [15] against the exact HAF susceptibility.…”

Section: Dmrg and Convergencementioning

confidence: 99%

“…Other systems sizes, including larger ones, can be studied. The numerical accuracy is ultimately limited by the density of low-energy states of large systems [15]. ED/DMRG exploits the fact that a few hundreds of states E p (α, N ) ≤ E C (α, N ) in sectors with S Z = 0, 1, ... suffice for the thermodynamics in a limited range of T at each system size.…”

Section: Dmrg and Convergencementioning

confidence: 99%

“…We obtain the thermodynamics by exact diagonalization (ED) of Eq. 1 in small systems of N = 4n spins and periodic boundary conditions followed by density matrix renormalization group (DMRG) calculations of the lowenergy states of larger systems of N ∼ 100 or more [15]. DMRG is powerful numerical method [16], now well established [17,18], for the ground state and elementary excitations of 1-D models.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Low temperature thermodynamics of the antiferromagnetic $J_1-J_2$ model: Entropy, critical points and spin gap

Saha,

Routh,

Kumar

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The antiferromagnetic J1 − J2 model is a spin-1/2 chain with isotropic exchange J1 > 0 between first neighbors and J2 = αJ1 between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with ∆(α) > 0 and doubly degenerate ground states. Exact thermodynamics is limited to α = 0, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration α followed by density matrix renormalization group (DMRG) calculations returns the entropy density S(T, α, N ) and magnetic susceptibility χ(T, α, N ) of progressively larger systems up to N = 96 or 152 spins. Convergence to the thermodynamics limit, S(T, α) or χ(T, α), is demonstrated down to T /J ∼ 0.01 in the sectors α < 1 and α > 1. S(T, α) yields the critical points between gapless phases with S (0, α) > 0 and gapped phases with S (0, α) = 0. The S (T, α) maximum at T * (α) is obtained directly in chains with large ∆(α) and by extrapolation for small gaps. A phenomenological approximation for S(T, α) down to T = 0 indicates power-law deviations T −γ(α) from exp(−∆(α)/T ) with exponent γ(α) that increases with α. The χ(T, α) analysis also yields power-law deviations, but with exponent η(α) that decreases with α. S(T, α) and the spin density ρ(T, α) = 4T χ(T, α) probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant S(T, α)/ρ(T, α) for T < 0.10. Remarkably, the ratio decreases (increases) with T in chains with large (small) ∆(α).I.

show abstract

Section: Introductionmentioning

confidence: 92%

“…We summarize the DMRG calculations in sectors with total 0 ≤ S Z ≤ N/2 presented in detail and tested in Ref. 15. The singlet ground state is in the S Z = 0 sector.…”

Section: Dmrg and Convergencementioning

confidence: 99%

Section: Dmrg and Convergencementioning

confidence: 99%

Section: Dmrg and Convergencementioning

confidence: 99%