A. P. Balachandran’s research while affiliated with Syracuse University and other places

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Publications (2)


Disorder-free localization in continuous-time quantum walks: Role of symmetries
  • Article

January 2024

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68 Reads

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1 Citation

Physical Review A

A. P. Balachandran

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We investigate the phenomenon of disorder-free localization in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation-symmetric many-fermion Hamiltonians and interpret them as generators of continuous-time quantum walks. When the number of fermions is very large we find that all the canonical basis states localize at all times, without the introduction of any disorder coefficients. This time-independent localization is not the result of any emergent disorder, distinguishing it from existing mechanisms for disorder-free localization. Next we establish the conditions under which the localization is preserved. We find that interactions that preserve and break the global permutation symmetry sustain localization. Furthermore, the basis states of systems with reduced permutation symmetry localize even for a small number of fermions when the symmetry-reducing parameters are tuned accordingly. We show that similar localization also occurs for a permutation-symmetric Heisenberg spin chain and permutation-symmetric bosonic systems, implying that the localization is independent of the superselected symmetry. Finally, we make connections of the Hamiltonians studied here to the adjacency matrices of graphs and use this to propose a prescription for disorder-free localization in continuous-time quantum walk systems. Many of the models proposed here feature all-to-all connectivity and can be potentially realized on superconducting quantum circuits, trapped ion systems, and ultracold atoms.


Localisation in Permutation Symmetric Fermionic Quantum Walks
  • Preprint
  • File available

July 2023

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55 Reads

We investigate localisation in a quantum system with a global permutation symmetry and a superselected symmetry. We start with a systematic construction of many-fermion Hamiltonians with a global permutation symmetry using the conjugacy classes of the permutation group SNS_N, with N being the total number of fermions. The resulting Hamiltonians are interpreted as generators of continuous-time quantum walk of indistinguishable fermions. In this setup we analytically solve the simplest example and show that all the states are localised without the introduction of any disorder coefficients. Furthermore, we show that the localisation is stable to interactions that preserve the global SNS_N symmetry making these systems candidates for a quantum memory. The models we propose can be realised on superconducting quantum circuits and trapped ion systems.

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Citations (1)


... Regarding transition probabilities, such calculations play a crucial role in, e.g. the context of localization [4], state transfer [13,19,20] and sedentary walks on graphs [21]. However, dissipation is usually absent from such contexts as the evolution is essentially unitary. ...

Reference:

One-dimensional continuous-time quantum Markov chains: qubit probabilities and measures
Disorder-free localization in continuous-time quantum walks: Role of symmetries
  • Citing Article
  • January 2024

Physical Review A