[Paper Review] Quantum phases of two coupled XXZ spin chains: A DMRG study

Bradraj Pandey, Supervisor Dr. Subhasis Sinha+1 more|arXiv (Cornell University)|Jun 23, 2014

Cold Atom Physics and Bose-Einstein Condensates1 citations

TL;DR

This study investigates quantum phases in two coupled one-dimensional XXZ spin chains with ferromagnetic inter-chain coupling using the density matrix renormalization group (DMRG) method. It identifies novel phases such as pair-superfluid and density wave of strongly bound pairs beyond conventional superfluid and charge density wave phases, offering a theoretical framework for realizing these in ultracold dipolar gases.

ABSTRACT

We consider hardcore bosons in two coupled chain of one dimensional lattices at half filling with repulsive intra-chain interaction and inter-chain attraction. This can be mapped on to a coupled chain of spin-1/2 XXZ model with inter chain ferromagnetic coupling. We investigate various phases of hardcore bosons (and related spin model) at zero temperature by density matrix renormalization group method. Apart from the usual superfluid and density wave phases, pairing of inter chain bosons leads to the formation of novel phases like pair-superfluid and density wave of strongly bound pairs. We discuss the possible experimental realization of such correlated phases in the context of cold dipolar gas.

Motivation & Objective

• To explore quantum phases in two coupled one-dimensional XXZ spin chains with repulsive intra-chain and attractive inter-chain interactions.
• To understand the emergence of unconventional quantum phases beyond standard superfluid and density wave states.
• To map the hardcore boson system onto a spin-1/2 XXZ model with ferromagnetic inter-chain coupling for theoretical analysis.
• To identify experimentally accessible phases in ultracold dipolar atomic gases via this spin model mapping.
• To provide a comprehensive phase diagram of correlated phases at zero temperature using DMRG simulations.

Proposed method

• Employing the density matrix renormalization group (DMRG) method to study the ground state properties of the coupled XXZ spin chain model at zero temperature.
• Mapping the hardcore boson system on a two-chain lattice with repulsive intra-chain and attractive inter-chain interactions to a spin-1/2 XXZ model with ferromagnetic inter-chain coupling.
• Using DMRG to compute order parameters, correlation functions, and energy spectra to distinguish between different quantum phases.
• Analyzing the system at half filling to explore the competition between superfluidity, charge ordering, and inter-chain pairing.
• Evaluating the stability and nature of novel phases such as pair-superfluid and bound pair density wave using correlation and pairing correlations.
• Comparing results with known phases to identify signatures of unconventional pairing and order.

Experimental results

Research questions

• RQ1 What quantum phases emerge in two coupled XXZ spin chains with repulsive intra-chain and ferromagnetic inter-chain interactions?
• RQ2 How does inter-chain pairing influence the formation of novel quantum phases beyond conventional superfluid and density wave states?
• RQ3 What are the distinguishing characteristics of the pair-superfluid and bound pair density wave phases in this system?
• RQ4 Can these phases be realized in experimentally accessible systems such as ultracold dipolar gases?
• RQ5 How do the phase boundaries and order parameters evolve with varying interaction strengths in the DMRG framework?

Key findings

• The system exhibits conventional superfluid and charge density wave phases, as expected from standard one-dimensional models.
• In addition to standard phases, the model supports novel phases such as pair-superfluid and density wave of strongly bound pairs.
• The pair-superfluid phase arises due to inter-chain pairing of bosons, leading to long-range off-diagonal order in the pair correlation function.
• The density wave of strongly bound pairs is characterized by a periodic modulation of the pair density with a wavelength of two lattice spacings.
• These novel phases emerge due to the competition between repulsive intra-chain and attractive inter-chain interactions, stabilized at half filling.
• The results suggest that ultracold dipolar gases in two-dimensional optical lattices could realize these correlated phases through tuning of dipolar interactions.