FOR 5522 PhD School on Nonergodic Quantum Dynamics

Entanglement-based approaches in studying highly correlated 1D spin systems using DMRG

Not scheduled

2h

HS 2 (Max Born Hörsaal) (Faculty of Physics)

Poster Session

Description

For my poster I would like to show recent works:

First part shows joined work [1] with Clio Agrapidis and Satoshi Nishimoto we investigate the low-energy properties of the dimerized frustrated ferromagnetic (FM) $J_1-J_1^{\prime }-J_2$ model with the density matrix renormalization group method. We show the ground state phase diagram spanned by a wide range of $J_1^{\prime }/J_1$ and $J_2/|J_1|$features ferromagnetic phase and valence bond solid (VBS) phases that are continuations from the $J_1^{\prime }/J_1$ limits of the model. In the limit $J_1^{\prime }/J_1$=1 we recover FM $J_1-J_2$ model hosting ${\mathcal{D}}_3$-VBS state where valence bonds form between third-neighbor spins. The other VBS phase named mixed-VBS features both second- and third neighboring spins that continue from the $J_1^{\prime }/J_1$=0 limit. We show that both phases feature hidden antiferromagnetic order and twofold degeneracy in the entanglement spectrum characterizing them as Haldane states. Remarkably, we encounter a nontrivial quantum phase transition between two topological VBS states, where at the boundary of phases VBS stability is enhanced.
We discuss results in the context of other spin chain models and edge-sharing cuprate materials.

Second part shows current cooperative work with Miłosz Panfil. We study the q-deformed Majumdar-Ghosh (qMG) [2] model. Beside magnetisation, energy gap or dimer order parameter we look how entanglement observables like von Neumann entropy, entanglement gap, central charge change under the influence of magnetic field. These measurements gave different perspectives on an unique system where commutation relations are broken by design and offer a bridge between:  transverse field Ising (integrable model) and Majumdar- Ghosh model (Heisenberg system projected from spin-3/2 to spin 1/2).

For now both models do not have established dynamics, however we intend to look for them later
motivated by results from [3] Phys. Rev. B 98, 235156 (2018) and [4] Phys. Rev. B 98, 235155 (2018), where the latter discusses strong ETH hypothesis.

References

[1] https://doi.org/10.1103/PhysRevB.108.205111
[2] https://doi.org/10.1142/S021797929400155X
[3] https://doi.org/10.1103/PhysRevB.98.235155
[4] https://doi.org/10.1103/PhysRevB.98.235156