We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual $s$ -wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and two-dimensional topological superconductors. This method leads to infinite families of locally interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional ${p}_{x}+i{p}_{y}$ superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual $s$-wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and two-dimensional topological superconductors. This method leads to infinite families of locally interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional ${p}_{x}+i{p}_{y}$ superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.

arXiv:1703.01249Physical review. B./Physical review. BSep 7, 201721 citations

Sixteen-Fold Way for Fermionic Topological Orders

Ryohei Kobayashi, Abhinav Prem, Matthew Yu

Fermionic topological orders can host 't Hooft anomalies with no bosonic counterpart. We identify a new sixteen-fold family of (2+1)D fermionic topological orders, forming a fermionic analogue of Kitaev's sixteen-fold way. This family is distinguished by the mod 16 't Hooft anomaly of a $\mathbb{Z}_2$ one-form symmetry, generated in each theory by a single nontrivial $\mathbb{Z}_2$ anyon. This intrinsically fermionic anomaly permits anyon spins that are forbidden in bosonic phases; the simplest new example is an Abelian fermionic topological order containing a single $\mathbb{Z}_2$ Abelian anyon of spin 1/8. Each theory can be realized as the gapped boundary of a (3+1)D fermionic symmetry-protected topological (SPT) phase protected by the $\mathbb{Z}_2$ one-form symmetry, which acquires a $\mathbb{Z}_{16}$ classification once the spacetime spin structure is twisted by the one-form symmetry. We realize these phases microscopically via lattice models built from Walker-Wang models coupled to local fermions.Fermionic topological orders can host 't Hooft anomalies with no bosonic counterpart. We identify a new sixteen-fold family of (2+1)D fermionic topological orders, forming a fermionic analogue of Kitaev's sixteen-fold way. This family is distinguished by the mod 16 't Hooft anomaly of a $\mathbb{Z}_2$ one-form symmetry, generated in each theory by a single nontrivial $\mathbb{Z}_2$ anyon. This intrinsically fermionic anomaly permits anyon spins that are forbidden in bosonic phases; the simplest new example is an Abelian fermionic topological order containing a single $\mathbb{Z}_2$ Abelian anyon of spin 1/8. Each theory can be realized as the gapped boundary of a (3+1)D fermionic symmetry-protected topological (SPT) phase protected by the $\mathbb{Z}_2$ one-form symmetry, which acquires a $\mathbb{Z}_{16}$ classification once the spacetime spin structure is twisted by the one-form symmetry. We realize these phases microscopically via lattice models built from Walker-Wang models coupled to local fermions.

cond-mat.str-elCross-listedarXiv:2606.28682Jun 30, 20260 citations

The Topological Phase Transitions Related to Fermion Condensate

M. Ya. Amusia, Konstantin G. Popov, Vasily R. Shaginyan +1 more

Springer series in solid-state sciencesOct 25, 20140 citations

Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice

Olivier Gauthé, Sylvain Capponi, Matthieu Mambrini +1 more

We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate $\mathbf{6}$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimerlike phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauth\'e, S. Capponi, and D. Poilblanc, Phys. Rev. B 99, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric projected entangled pair states (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations.We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate $\mathbf{6}$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimerlike phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauth\'e, S. Capponi, and D. Poilblanc, Phys. Rev. B 99, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric projected entangled pair states (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations.

arXiv:2002.05572Physical review. B./Physical review. BMay 26, 202014 citations

TOPOLOGICAL PHASE TRANSITIONS IN STRONGLY CORRELATED FERMI SYSTEMS

J. W. Clark, VICTOR A. KHODEL, MIKHAIL V. ZVEREV

Dec 1, 20090 citations

s

-wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and two-dimensional topological superconductors. This method leads to infinite families of locally interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional

{p}_{x}+i{p}_{y}

superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.

\mathbb{Z}_2

one-form symmetry, generated in each theory by a single nontrivial

\mathbb{Z}_2

anyon. This intrinsically fermionic anomaly permits anyon spins that are forbidden in bosonic phases; the simplest new example is an Abelian fermionic topological order containing a single

\mathbb{Z}_2

Abelian anyon of spin 1/8. Each theory can be realized as the gapped boundary of a (3+1)D fermionic symmetry-protected topological (SPT) phase protected by the

\mathbb{Z}_2

one-form symmetry, which acquires a

\mathbb{Z}_{16}

classification once the spacetime spin structure is twisted by the one-form symmetry. We realize these phases microscopically via lattice models built from Walker-Wang models coupled to local fermions.

We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate

\mathbf{6}

representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimerlike phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauth\'e, S. Capponi, and D. Poilblanc, Phys. Rev. B 99, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric projected entangled pair states (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations.