In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). MQMC simulations can be performed efficiently both at finite and zero temperatures. Especially, MQMC is fermion sign free in simulating a class of spinless fermion models on bipartite lattices at half filling and with arbitrary range of (unfrustrated) interactions. Moreover, we find a class of SU (N ) fermionic models with odd N , which are sign-free in MQMC but whose sign problem cannot be in solved in other QMC methods such as continuous-time QMC. To the best of our knowledge, MQMC is the first auxiliary field QMC method to solve fermion sign problem in spinless (more generally, odd number of species) fermion models. We conjecture that MQMC could be applied to solve fermion sign problem in more generic fermionic models.Introduction: Interacting fermionic quantum systems with strong correlations and/or topological properties have attracted increasing attentions [1,2]. Nonetheless, in two and higher spatial dimensions, strongly interacting quantum systems are generically beyond the reach of analytical methods in the sense of solving those quantum models in an unbiased way. As an intrinsicallyunbiased numerical method, quantum Monte Carlo simulation plays a key role in understanding physics of strongly correlated many-body systems [3][4][5][6][7]. Unfortunately, in simulating fermionic many-body systems, QMC often encounters the notorious fermion minus-sign problem [8,9], which arises as a consequence of Fermi statistics [10]. Undoubtedly, generic solutions of fermion sign problems would lead to a great leap forward in understanding correlated electronic systems [9].Many QMC algorithms are based on converting an interacting fermion model into a problem of free fermions interacting with background auxiliary classical fields; the Boltzmann weight is the determinant of free fermion matrix which is a function of auxiliary fields and which can be positive, negative, or even complex. In such determinant QMC (DQMC), when the determinants are rendered to be positive definite, we say a solution to the fermion sign problem is found. For spinful electrons, conventional strategy of solving fermion sign problem is to find a symmetric treatment of both spin components of electrons such that the Boltzmann weight can be written as the product of two real determinants with the same sign and is then positive definite [11][12][13][14][15][16]. For spinless or spin-polarized fermion models, it is usually much more difficult to solve fermion sign problem because the Boltzmann weight contains only a single determinant and the usual strategy used for even species of fermions cannot be directly applied here.In this paper, based on Majorana representation of fermions, we propose a genuinely new auxiliary field QMC approach to solve fermion sign problem in spinless fermion models. We observe that each complex fermion

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Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo method introduced by us in (Li et al 2015 Phys. Rev. B 91 241117), we investigate the quantum critical phenomena of spinless Dirac fermions at their charge-density-wave phase transitions on the honeycomb lattice having N L 2 s 2 = sites with largest L = 24. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of two (twocomponent) Dirac fermions in 2+1D: 0.45(2) η = , 0.77(3) ν = , and 0.60(3) β =, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.

A unified theory of quantum critical points beyond the conventional Landau–Ginzburg–Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau–Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.

The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many body physics. The conventional superconductors are insensitive to dilute nonmagnetic impurities, known as the Anderson's theorem 1 .Destruction of superconductivity and even superconductor-insulator transitions 2-10 occur in the regime of strong disorder. Hence disorder-enhanced superconductivity is rare and has only been observed in some alloys or granular states 11-17 . Because of the entanglement of various effects, the mechanism of enhancement is still under debate.Here we report well-controlled disorder effect in the recently discovered monolayer

A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anticommuting MTR symmetries they respect, we rigorously prove that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class," respectively. Novel sign-problem-free models in the Majorana class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly correlated systems and interacting topological matters.

Monolayer FeSe films grown on SrTiO3 (STO) substrate show superconducting gap-opening temperatures () which are almost an order of magnitude higher than those of the bulk FeSe and are highest among all known Fe-based superconductors. Angle-resolved photoemission spectroscopy observed “replica bands” suggesting the importance of the interaction between FeSe electrons and STO phonons. These facts rejuvenated the quest for enhancement mechanisms in iron-based, especially iron-chalcogenide, superconductors. Here, we perform the first numerically-exact sign-problem-free quantum Monte Carlo simulations to iron-based superconductors. We (1) study the electronic pairing mechanism intrinsic to heavily electron doped FeSe films, and (2) examine the effects of electron–phonon interaction between FeSe and STO as well as nematic fluctuations on . Armed with these results, we return to the question “what makes the of monolayer FeSe on SrTiO3 so high?” in the conclusion and discussions.Electronic supplementary materialThe online version of this article (doi:10.1007/s11434-016-1087-x) contains supplementary material, which is available to authorized users.

Reliable simulations of correlated quantum systems, including hightemperature superconductors and frustrated magnets, are increasingly desired nowadays to further understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically-exact and intrinsically-unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion-sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously-broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progresses made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.