Theoretical approaches for strongly correlated systems

In order to investigate anomalous features in strongly correlated systems, I have applied exact solutions and unbiased numerical techniques.

 Analytical methods

• Bethe ansatz (exact solutioins)
- Dispersion relation E(k)
- Dynamical structure factor S(k,ω)

• Proof of the exact ground state
- Proof using the Perron-Frobenius theorem

• Perturbation theory
- Ramdom phase approximation (RPA) with respect to interchain coulpings
- Expansion with respect to inter-rung hopping
- Expansion around the Ising limit

• Scaling analysis

 Numerical methods

• Quantum Monte Carlo
- Cluster algorithm
- (directed) loop algorithm
- Auxiliary-field Monte Carlo
- Power-Lanczos Monte Carlo

• Density -Matrix Renormalization Group (DMRG) method
- Ground state
- Dynamical DMRG method [spectral function A(k,ω)]
- Non-Abelian dynamical DMRG method

• Cluster Perturbation Theory (CPT)
• Path-Integral Renormalization Group (PIRG) method
• Exact Diagonalization method
- Lanczos method
- Level Spectroscopy

• Maximum Entropy