xxz chain
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Author(s):  
John S. Van Dyke ◽  
Edwin Barnes ◽  
Sophia Economou ◽  
Rafael I Nepomechie

Abstract The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of (L M) 2M M! terms, the algorithm requires L + M2+ 2M qubits.


2021 ◽  
Vol 104 (20) ◽  
Author(s):  
Yuhi Tanikawa ◽  
Hosho Katsura
Keyword(s):  

2021 ◽  
Vol 104 (20) ◽  
Author(s):  
Yankang Liu ◽  
Yohei Fuji ◽  
Haruki Watanabe
Keyword(s):  

2021 ◽  
Vol 62 (10) ◽  
pp. 101901
Author(s):  
Christoph Fischbacher ◽  
Oluwadara Ogunkoya

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Yuan Miao ◽  
Jules Lamers ◽  
Vincent Pasquier

The spin-\frac{1}{2}12 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We construct Baxter’s Q operator at arbitrary anisotropy from a two-parameter transfer matrix associated to a complex-spin auxiliary space. A decomposition of this transfer matrix provides a simple proof of the transfer matrix fusion and Wronskian relations. At root of unity a truncation allows us to construct the Q operator explicitly in terms of finite-dimensional matrices. From its decomposition we derive truncated fusion and Wronskian relations as well as an interpolation-type formula that has been conjectured previously. We elucidate the Fabricius–McCoy (FM) strings and exponential degeneracies in the spectrum of the six-vertex transfer matrix at root of unity. Using a semicyclic auxiliary representation we give a conjecture for creation and annihilation operators of FM strings for all roots of unity. We connect our findings with the `string-charge duality’ in the thermodynamic limit, leading to a conjecture for the imaginary part of the FM string centres with potential applications to out-of-equilibrium physics.


2021 ◽  
Vol 54 (41) ◽  
pp. 414001
Author(s):  
Frank Göhmann ◽  
Raphael Kleinemühl ◽  
Alexander Weiße
Keyword(s):  

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