1. hybrid exact diagonalization and density matrix renormalization group approach to the thermodynamics of low-dimensional interacting quantum systems

Sudip Kumar Saha

Satyendra Nath Bose National Center for Basic Sciences, India

16 December 2021 Thu 5.30 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

The quantum many body model Hamiltonians are used in modeling electronic properties of real materials and understanding exotic phases in low dimensional condensed matter systems. However, solving these model Hamiltonians is difficult due to exponential growth of the Hilbert space with system size and calculating even the exact ground state (gs) properties of these systems is impossible in the majority of cases. To explain the experimental results at finite temperature (T) the full spectrum and their wavefunctions of the model Hamiltonian are required. There are many numerical methods to solve the thermodynamic properties of these correlated systems, unfortunately all these methods have their own limitations.

Inspired by the need of a general method to solve eigenvalues and eigenvectors a low dimensional quantum many body model Hamiltonian, we develop a hybrid exact diagonalization and density matrix renormalization group approach, and this method can calculate the thermodynamical properties of strongly correlated 1D models. At the high T, correlations between the electrons are suppressed by thermal fluctuations and results at the thermodynamic limit can be achieved just by solving a small system size. However, the study of thermodynamics at low T requires larger systems to reach the thermodynamic limit due to presence of large correlation length. The partition function is the sum of the Boltzmann probability of all energy states, and has a significant contribution from low energy states at low T. The higher excited states have exponentially small contributions, therefore, the accurate low T properties require only accurate low-lying energy states. The density matrix renormalization group (DMRG) method is well known for its accurate calculation of low- lying states and can be employed to give accurate results in low T limits. The hybrid ED/DMRG method does not require full spectrum for large system size, therefore, it may be used as a general method for calculating the thermodynamic properties of one dimensional correlated systems.

The hybrid ED/DMRG results for exactly solvable models like Heisenberg antiferromagnetic spin- 1/2 and non-interacting tight binding models are benchmarked . We also benchmark this method for models like the frustrated spin-1/2 J1−J2 model. To establish it as a general method for one dimensional correlated systems, its application is extended to the fermionic system with active spin and charge degrees of freedom. We are able to demonstrate the separation of spin and charge excitations at large onsite Hubbard U in a half filled Hubbard model. This method also enables us to show the different low T behavior of thermodynamic quantities at spin density wave phase, bond order wave phase and charge density wave phase in half-filled extended Hubbard model (EHM). Furthermore, the method offers scope to explore the fermionic systems away from the half-filling where most of the numerical methods fail to give accurate results. We have also successfully shed light into the long-standing problem of the spin-Peierls (SP) transition in organic TTF-CuS4C4(CF3)4 and inorganic CuGeO3 using correlated models.

Related Publications:

1. Hybrid exact diagonalization and density matrix renormalization group approach to the thermodynamics of one-dimensional quantum models, Sudip Kumar Saha, Dayasindhu Dey, Manoranjan Kumar, and Zoltán G. Soos, Physical Review B 99, 195144 (2019).

2. Modeling the spin-Peierls transition of spin- 1/2 chains with correlated states: J1−J2 model, CuGeO3, and TTF−CuS4C4(CF3)4, Sudip Kumar Saha, Monalisa Singh Roy, Manoranjan Kumar, and Zoltán G. Soos, Physical Review B 101, 054411 (2020).
3. Bond-bond correlations, gap relations and thermodynamics of spin-1/2 chains with spin- Peierls transitions and bond-order-wave phases, Sudip Kumar Saha, Manoranjan Kumar, and Zoltán G. Soos, Journal of Magnetism and Magnetic Materials 519, 167472 (2021).
Density matrix renormalization group approach to the low temperature thermodynamics of correlated 1d fermionic models, Sudip Kumar Saha, Debasmita Maiti, Manoranjan Kumar, and Zoltán G. Soos, arXiv:2101.04362 [cond-mat.str-el] (2021).
Low temperature thermodynamics of the antiferromagnetic J1−J2 model: Entropy, critical points, and spin gap, Sudip Kumar Saha, Manodip Routh, Manoranjan Kumar, and Zoltán G. Soos, Physical Review B 103, 245139 (2021).